Firstly, each of your example sentences talks about a male. But they do not talk about the male in the same way. So, you can't really use these two grammatically different example sentences to prove the same grammatical point.
To explain ...
In the first sentence, "I saw him riding a bike," the identity of the male is already established, and he (the object of the sentence, therefore "him") happened to be riding a bike when the speaker saw him.
Is this the same as "When I saw him, he was riding a bike"?
Well, it depends on the context. If the conversation is about whether the male in question can ride a bike or not, then "I saw him riding a bike" and "When I saw him he was riding a bike" both affirm that he can, indeed, ride a bike.
However, maybe the situation is a police suspect line-up. The police asks "Which of these men was riding a bike?" The person points to one of the suspects and says "I saw him riding a bike." The person would not say "When I saw him he was riding a bike" because the identity of "him" has not been established yet.
As for the second sentence...
"The guy shouting at his wife looks familiar" is quite different from "The guy is shouting at his wife and he looks familiar."
In "The guy shouting at his wife looks familiar," the identity of the male has not yet been established. Rather, this sentence works to identify him (the subject of the sentence, therefore "he"), which it does by identifying him as the male who is shouting at his wife (as opposed to other males present who are not shouting at their wives).
On the other hand, in "The guy is shouting at his wife and he looks familiar," we already know who the guy is. The use of "the" identifies him as someone who we have already encountered in prior conversation leading up to this sentence.
So, the different grammar here doesn't allow a single answer to your question.
(Incidentally, I don't understand what you mean by "I know that those sentences fit Simple Tenses just fine and I wouldn't use a Continuous Tense in these cases." Do you mean writing them as "I saw him ride a bike" and "The guy who shouts at his wife looks familiar"? If so, then, no, their meaning changes.)