Does this mean "game over" for the GOP if Texas is lost?
For a couple of cycles, yes.
You mean for like a couple of decades or 12 to 16 years at most? Is conservatism lost then?
I would say two to four elections.
Depends on what you mean by "Conservatism". Conservatism always has a way of coming back within the confines of new political context. If by Conservatism you mean the movement which has for the past 30 years dominated Republican politics and takes to using that term to describe itself, then to an extent yes but that has a lot more working against it than just Texas turning purple/blue.