First, it important to note that the confusion surrounding this subject is largely due to the tunnel-vision perspective of Tarot enthusiasts. Tarotists think of everything in terms of Tarot. In the larger world, there are things other than Tarot.
1. Presumably by mentioning Michelino you mean to refer to the unique deck and game described by Jacopo Marcello, the 16-Heroes deck created by Marziano da Tortona for Filippo Maria Visconti. This was not a Tarot deck, nor does it have any direct connection with Tarot. The designer and artist may have some other connection with Tarot, and certainly the Patron and the milieu had a lot to do with Tarot. However, this deck was a unique production, a unique conception of trumps, and the structure of the deck, the subject matter of the trumps, and the game played, appear to have contributed nothing to Tarot. It is not quasi-Tarot nor proto-Tarot, but simply a different type of deck and game, one that left no descendants. The world of playing cards consists almost entirely of things other than Tarot, and this is one of them.
Oh, well, there are various tunnel-perspectives in matters of Tarot.
First ... it would be logical to call something "Tarot", which the speakers of their time called "Tarot".
As we know, this similar "Taraux" or "Tarocchi" appeared to our eyes in the year 1505 in France and Ferrara, Italy, for the first time. If we wish to define "Tarot" in this way, then we could skip luckily all 15th century predevelopments of the cards from the table and say, "that's it".
Now in Tarot history research has developed the opinion, that the objects called "Trionfi" or similar in 15th century (as far they are playing cards) refered to that object, which later was called Tarot. So it became custom to imagine, that, whenever in documents the name "Trionfi" (or similar) appeared, that this reference should belong to that, what the reader imagined was "Tarot" (and most readers imagined for Tarot a game structure of 21+1+56 cards and a specific set of motifs).
However, there is evidence, that this idea went definitely wrong ... at a few
occasions it could be proven, that the objects called Trionfi (or similar) in documents definitely hadn't the refered game structure and also not the specific set of motifs (Michelino deck, document of 1457).
So the elegant translation solution "Tarot (of ca. 1505) = Trionfi (of 15th century", which seemed to offer an understanding of these sentences in 15th century documents, was not operating correctly and has to be replaced by the simple research question "Trionfi ? - what kind of deck might have been meant at this occasion in this document ?".
Now there is to exspect, that something was similar between all these mentioned Trionfi decks in 15th century - but what?
From the examples, that we know, we know, that the motifs weren't stable (Boiardo, Sola Busca) nor that the structure was stable (Michelino deck; note of 1457; Cary-Yale).
The name "Trionfi" signals "trumps" - indeed we can identify a trumps-series in the Taraux-concepts, which are assumable for the year 1505. So we could perhaps expect a series of trumps in all these objects, which are called "Trionfi" (or similar ) in documents of 15th century.
Indeed this definition would work (for instance also for the Michelino deck) and it would make the Taraux (of 1505 and later) just to a special case of the more generally named Trionfi deck, a subcategory with the signifying feature of a 21+1+56-game-structure.
In this case: "Dear Tarot, get your ass out of 15th century, you weren't born then" ... .-)
But, what shall we say, in 15th century are things, which are similar to Tarot, just as parents look similar to their children or vice versa.
So what? Reality isn't changed by calling it Paul or Peter. There are certain objects, which demand to be studied at their individual occasion and their individual context, written documents and cards, anything is useful. The informations about the Michelino deck are one of the oldest texts of playing card history, important in themselves and they don't ask Michael Hurst, if they should be called Tarot or Trionfi deck - a classifying system is only of interest for the human mind and only of interest, if it works and helps to keep the observed development process sorted.
Actually - as I interprete it - the interesting question is, how Tarot developed and what of the known informations can help to understand the process. As the Michelino deck appeared at the same court before the appearance of the first decks, which have iconographic similarities to the later Tarot (the Michelino deck has only structural similarities), it's obviously of great interest and delivers precious informations.
Generally the wish to explore Tarot's birth and departure from the normal playing card deck (and it's a general opinion, that normal playing cards came first and Tarot developed from it) should lead to a playing card deck-form, which has one leg in the normal playing card structure and another leg in something, which is similar to Tarot. Actually such a deck gives the signal, that research is with such an object near to the desired "birth-place of Tarot", and that this deck is found at the same place and court as the "examples near in iconography" (Cary-Yale, Brera-Bambilla) is "ideal as it could be". Better evidence is hardly possible in the given situation.
***
Just for this sentence from Michael about the Michelino deck informations:
"However, this deck was a unique production, a unique conception of trumps, and the structure of the deck, the subject matter of the trumps, and the game played, appear to have contributed nothing to Tarot."
* It's the first clear report of "trumps" ... and trumps are essential for the Tarot.
* Also it's the first report of a hierarchical row of trumps, also essential for Tarot
* As far it gives informations about the game (which are not too much), it describes elements, which also appear in Tarot.
****
Martiano da Tortona:
"Consider therefore this game, most illustrious Duke, following a fourfold order,
= 4 suits
by which you may give attention to serious and important things, if you play at it. Sometimes it is pleasing to be thus diverted, and you will be delighted therein. And it is more pleasing, since through the keeness of your own acumen you dedicated several to be noted and celebrated Heroes, renowned models of virtue, whom mighty greatness made gods, as well as to ensure their remembrance by posterity.
= iconography of the trump pictures
Thus by observation of them, be ready to be aroused to virtue.
Indeed the first order, of virtues, is certain: Jupiter, Apollo, Mercury and Hercules. The second of riches, Juno, Neptune, Mars and Aeolus. The third of virginity or continence: from Pallas, Diana, Vesta and Daphne. The fourth however is of pleasure: Venus, Bacchus, Ceres and Cupid. And subordinated to these are four kinds of birds, being suited by similarity.
= description of suits
Thus to the rank of virtues, the Eagle; of riches, the Phoenix; of continence, the Turtledove; of pleasure, the Dove. And each one obeys its own king. However, the order of these Birds is, although none of their type has right over another, yet this arrangement they have alternately – Eagles and Turtledoves lead from many to few: that is to say it goes better for us when many cultivate virtue and continence; but for Phoenices and Doves, the few rule over the many, which is to say that, the more the followers of riches and pleasure are visible, the more they lead to the deterioration of our station.
= description, that two suits run in their hierarchy (probably) from 1-10 and the other two from 10-1 (typical for Tarot)
Every one of the gods, however, is above all the orders of birds and the ranks of kings.
= declaration of the trumps (16 trumps)
But the gods are held to this law among themselves: that who will be first designated below, he should lead all the others following in sequence.
= declaration of the hierarchical trumps row (typical for Tarot)