For all of the fans of the original board game, all of the core mechanics are present. You're still visiting certain locations for a higher rate of return on certain types of items, you are still managing your cult to send them to different locations, gaining control of areas, etc. You can only use your God's gift in areas you control.
In addition, raids still occur once investigators have become too suspicious of you. Traveling via portal to a location still requires sacrificing of a spell with the correct alignment (color). Areas that you've visited recently will become more concentrated with Investigators who are suspicious of you (making it much harder for you to go to these locations, and much more likely that your cultists will be found).
You still summon your Elder God when you've reached a critical amount of Eldritch power. The game still finishes when you summon your Elder God. It's just changed slightly to be that you likely summon your Elder God at the end of the story-line for that cult's quest arcs (though, even this is up to you and how you play the game). Other cults can rise up to banish your summoned God, so you'll have to strategically plan when to do it, and stop them from getting the things they need to succeed in their summoning (whether you're playing single-player or multi-player).
As it's an action video game, there are many ways we've expanded gameplay, as well. But, all of the core mechanics of the board game are still present.