watch his girlfriend talking to another guy.
or use the word while
watch while his girlfriend is talking
For clarity, you should not use he and him to refer to different people in the same sentence. The fact that you needed to clarify another guy shows the problem. Although we might be able to infer the meaning we can't be sure which he/him is which person. Going a step further we also have his in the sentence, and we need to make sure there is no ambiguity about which person's girfriend this is.
So we say
How could Bill watch his girlfriend talking to another guy?
or, if we've very recently had other references to Bill, so it's very clear who he is,
I've never understood Bill.
How could he watch his girlfriend talking to another guy like that?
Now in speech we could use our vocal inflections to indicate that he and him are different people.
How could he just watch his girfriend talking to (rising inflection, emphasis) him.
But when writing, or speaking in a more formal context, take special care to ensure that it is clear which he or him you mean.