The name is the most important part, as it gives them a way to look for games that have their name but aren't theirs. But you're mostly right that they actually go after any game that has the same gameplay and is relatively popular, but only when they can easily issue a DMCA takedown. It's not like they ever said that this was their policy but you can see it bear out time and again.
TETR.IO and Jstris are insanely popular games that have been up for years with no action against them since they aren't hosted on another platform/marketplace.
This is also why Apotris got 2 DMCA takedowns on both Github and itch.io 3 months apart from each other, but after hosting the game on my own site, they haven't taken any further action in the past 2 years while it has continued to grow in popularity.
TETR.IO and Jstris are insanely popular games that have been up for years with no action against them since they aren't hosted on another platform/marketplace.
This is also why Apotris got 2 DMCA takedowns on both Github and itch.io 3 months apart from each other, but after hosting the game on my own site, they haven't taken any further action in the past 2 years while it has continued to grow in popularity.