Yes it very much still applies.  You still need culture points to unlock the perks.  The difference is now the trees are linear each perk in the tree has to be unlocked in order and costs multiple points per unlock unlock the single point previously.  

By default you gain one point per turn, points you earn from events get added to the total.  Increasing cultural awareness is also still valuable as now it gives you a discount in the cost of each point in that particular the.

I think it's a better system now because if you want a perk near the end of a tree you really have to commit to that cultural tree in terms of event choices.

Hope this helps.