Is "he runs like a cheetah" a kind of metaphor?

"He is a cheetah" is indeed a metaphor, as in fact he is not a cheetah.

"He runs like a cheetah" is more precisely a simile, even if he does not copy every part of the cheetah's style of running, because of the explicit comparison using like.

Both suggest he is fast. Either will probably convey your message.

I think we can safely say both "He is a cheetah" and "He runs like a cheetah" are metaphoric.

The first more so, since presumably "he" is a human being. But he doesn't run on all fours like a cheetah (or as fast, if we're honest!), so he's only metaphorically running like one.

If OP wants to "make" a metaphor, he can use the first form. It will have been said many times before, I'm sure, but I certainly wouldn't call it a cliche.

The second form has probably been used even more often, so if OP only wants to "use" a metaphor, that may be the one to go for.