The phrase "games that have us like" makes sense, but it's an incomplete thought.
The meaning of the phrase "games that have us like, 'whoa'" (or however you might spell that) is games that when played, or watched, made us react with astonishment.
More generally, the phrase "[noun/pronoun] has us like [reaction]" means the noun/pronoun caused us to feel the stated way.
For example, a quick search turns up these two results:
"[Her] booty has me like, whoa" - when I see her butt, I am astonished
"Instagram stories got me like, you all need to listen to better music" - when I see your Instagram stories, I feel like you need to listen to better music.
This construction is slang and should only be used in contexts where slang is appropriate.
So, "games that have us like" makes sense, but demands more information, just the same as the phrase, "books that make us think of" - think of what?