The most basic definition of stoicism is "indifference to fate". In that scope Taleb definitely is a stoic. His approach toward stoicism, though, is less philosophy focused and more (that's kind of unique) targeted toward statistics. Ancient stoics don't write about their philosophy in such a way, but the logic remains similar. The whole concept of antifragility Taleb has promoted is pure "opportunistic" stoicism. Taleb is like a Seneca the Younger, minus some charm ;)

Regarding his online presence, anyone knowing his works also knows that he's using Twitter purely to mess with people. He stated that many times in his Incerto series.

Sometimes it's easy to forget what is the actual core of a given philosophy / enterprise / etc. Hence my whole comment. It's worthwhile to know, I think, that stoicism has a very important component comprised of pure logic, which Taleb seems to be hyped about (not without a reason).

I wouldn't call Taleb a member of the top-3 stoics though. He's balancing on the verge of being an outcast rather than hanging out with mainstream stoic crowds.