Does survival games come with minecraft game?

Yes! When you get minecraft you are automatically able to play survival games. I know this because i play survival games myself and it is the funnest thing about minecraft. If you want to play survival games you must sign in to minecraft and then click on the multiplayer gui button. One you click on multiplayer then you must go to add servers and add any hunger games server that you want to play.

The three best hunger games servers in my mind are:

Mcthefridge: which you can get in from typing- sg1 all the way to sg36.mcthefridge.com individually

MCSG: which you can get into from typing- us1 all the way to us91.mcsg.in each individually

MCHive: which you can get into from typing- HiveMC.eu just once to get into the hub and then get into your desired game by clicking a sign the is labeled lobby in the survival games section of the hive.

I really hope that this answer helps you out!

Survival is a mode within minecraft itself where there are monsters and a hunger meter and such.
So yes it comes with it, the other mode is called creative.