You either have a data connection and don't realize it or it's stuff that's programmed into the game already and only sounds like it's some sort of update.
The alerts are likely built into the Apps and don't need a data connection. If you click the links nothing will happen, or the Play Store will fail to open. I'd still say there is an issue with that App, as it shouldn't be spamming you like that.
i will list the apps which sends me notifications:
asphalt 7
asphalt 8
word search
deer hunter
injustice - gods among us
cookie clickers
plant vs zombies 2
tap the frog
tap the frog doodle
Do you actually have those apps? It looks more like an ad service pushing notifications. If you're on a recent version of Android, you should be able to long-press the notifications. Tap the "App info" button that pops up. It will take you to the device settings page for the app that's sending you the notifications. Uninstall it or uncheck "Show notifications" and the notifications should stop.