Well, I know very little about the game (I'm not Czech and so wasn't ever taught to play it), but here are a few thoughts off the top of my head - sorry it's all a bit quick and sketchy for now.
There are quite a lot of local references to tarot as a divination tool from around the late 19th century onwards (e.g. notoriously in Meyrink's 1915 "Gollum"). In fact we've been dithering about buying a hand-drawn set of cards (very expensive as the artist is well-known) which seem clearly to have been for divination purposes and which are probably (though hard to be sure until we can do some research) from around 1900. BUT, interesting as all this is, of course it's centuries later than the period you're talking about. I don't want to derail the thread, but if you want to talk separately about this later history of tarot on another thread, then that might be very interesting. Much of the later "occult" tarot history here was for years sadly neglected - for obvious reasons.
What may be more relevant to the immediate question is a pack of cards (but pretty clearly for gaming purposes IMO) that are reproduced in the "Powder Tower" museum here, and which are claimed (on whose authority I don't know) to be from around the time of Rudolph II - i.e. early. However, it's a bit of a tourist museum and I wouldn't take this at face-value necessarily. Next time I'm up there I'll take another look at them and even photograph if possible - but can't promise to do this soon I'm afraid.
You will find a reference in "Magic Prague" (a classic by Ripellino
http://www.amazon.com/exec/obidos/ISBN=0520073525/ref=nosim/aeclectic/) to tarot cards being used for divination at Rudolph's court. However, this assertion seems to be based on nothing - sheer romanticism I'd say.
The whole situation is somewhat complicated by the fact that there is a distinctly Czech/Moravian game that by my understanding is "tarot-like" rather than tarot - it has suits but no trumps. It's described at Andy's Playing cards:
www.geocities.com/a_pollett/cards13.htm
(I can't get this link to work as it says it's "exceeded its quota" - hopefully it will work soon.)
Incidentally, the descriptions here of the use of tarot and tarot-like cards in this region is excellent - but I'm sure you already know it.
The pack used is 32 cards (usually) and the cards are very evocative and fairly unique. We used elements from them in our Tarot of Prague by the way (we wanted, in part, to evoke gaming cards and their history). When people talk about Czech tarot, they seem sometimes to be referring to the game known across Europe (often played here with Austro-Hungarian pattern cards) and sometimes to this 32-card game. This can be confusing.
One final thought. "The" academic book on Russian magic is "The Bathhouse at Midnight"
http://www.amazon.com/exec/obidos/ISBN=0271019670/ref=nosim/aeclectic/
It is an excellent, exhaustive survey (very much someone's published doctoral thesis, so a fairly dry read, but beautifully researched). It has very little reference to the use of divinatory cards until, again, the later centuries. I will go look tonight and give you some details. I think if there had been ANY verifiable evidence of the use of cards for divination (by Royals, Roma or whatever) early on in Russia, the author of this book would have discovered them. Of course, he does not concern himself with playing cards.
My feeling is that there is little evidence for tarot as a divination tool here (or further east) until around the time it began to emerge as such all over Europe. As far as the game is concerned, then yes, it probably was here - remember that there was a lot of contact between Prague and other capitals, including Madrid and Rome.
One final thought. I have been trying for a while to get to meet the leading authority on Roma belief and magic here (she is a very busy university academic). If/when I succeed, I will of course ask her about how far back she thinks the Roma use of cards goes. Again though, apologies if this is not specific to your question (but it is ever so interesing!)