Are points still a relevant mechanic? When talking about gamification people's mind almost immediately go to points. It is probably the quintessential mechanic.

However, thinking of games, it's no longer heavily used. It's still in use but doesn't seem to be a main driver in most games. While people may have cared about high scores in Pac-Man or Donkey Kong, many modern games either don't use points at all or have them but players seem to not really pay too much attention to them.

Have their been any studies regarding the efficacy of using points in a gamified system or their performance against any alternatives?
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.