Minecraft mini games on ps4?

Kind of, you won't get the mini games like on PC as that is done using plugins which the PS4 can't do.

However you can setup your own mini games but they won't be near as good as PC, for hunger games simply make a map and place chests around the place (if you want loot anyway) and when someone dies simply make them wait in a lobby area. There's no way of controlling that.

You can do now spleef, create an arena with a floating TNT floor. Give everyone a bow with at least flame 1 so that they can set off the TNT.

If you're good with red stone then you can make your own mini games, I created one which involves multiple of floating island with buttons around the place. The guy on the other island has to try and shoot the other islands buttons which will open a gap in the floor. Last person alive wins.

You can't play mini games (or servers) on any console version of Minecraft. That is all exclusive to the PC version.

But if you want to play something you want to set up, like Hunger Games, you and a friend can build a map, invite tons of other friends, and play. Just exit without saving after finished with the map.

Also if you are good with redstone, you can make GENIUS creations. But technically you can play any PC mini game that you are able to build.