Wir haben zu arbeiten.

English Translation

We have work to do.

Would “Wir haben zu spielen” work for “We have games to play”? In other words, if the noun and the verb are similar enough, “tun” can be dispensed with?

“Wir haben zu arbeiten” means “we must work”.
With “spielen” this is a strange sentence, although a precocious five-year-old might say that.
On the other hand “wir haben zu essen” means “we have (something) to eat”.

“Wir haben zu tun” is more colloquial and means “we must do something”,

You cannot say “wir haben Spiele zu tun”.

Compare my comment in Ich habe Geld in einen Safe getan. - #2 by MRgK