Are points still a relevant mechanic?
Hmm. It's possibly I'm misunderstanding, in which case I will happily retract my answer. But does gamification really apply to, well, games? I thought the idea behind gamification was to take user engagement elements present in games and add them into non-gaming situations to increase user retention/satisfaction etc. 

So I would say that if you're making a game, you're not using gamification. You're making a game, which inherently has some of these characteristics. After all it's called gamification because the concepts were borrowed from games, right?

That said, to answer your question, I think points are still valuable in games when they're used as currency. When you can use the points to get stuff, that adds a whole new level of value.