I agree. A big part of the valuation of twitch.tv is it's positioning in the market. It doesn't make sense to drastically shock that positioning while locking out a large contingent of users in the process.
If Amazon wanted a similar service to make exclusive to the Kindle ecosystem, it would make much more sense to grow one themselves with deep integration into the kindle line of products. They've done this with a lot of other products and services, and certainly have the capability.
With Twitch, it would seem to make more sense for them to continue to seek partnerships with gaming platforms so that the Twitch.tv brand is increasingly ubiquitous in gaming, and then use that as a relatively extrinsic source of growth.
I could see them locking out strategic players (hint: Google), and making certain events or content exclusive to the Kindle ecosystem, but locking everything down to Kindle doesn't strike me as a viable move.
Yes I think this is critical. You just don't buy Kindle stuff for games or you're going to be not only disappointed but at a terrible disadvantage because of the artificial lock-in. The Amazon App Store is much smaller than Play and iTunes (though improving), and the Fire TV has a very small and stagnant selection of games (and not really improving).
