Is "I never saw him yesterday" grammatical, used to mean that "at no point in time in yesterday did I see him"? Does the sentence sound weird to a native speaker of AmE?
I didn't see him yesterday
is a more standard way to express the basic idea.
I never saw him yesterday.
We would normally use never saw in this way only when there is a special reason to do so.
As Adam and gnasher729 point out or suggest, the reason for doing so is to communicate contrast.
For example, many prior occasions contrasted with none
Although I saw him several or many times before yesterday, I saw him zero times yesterday.
Or a lengthy period in which I might have seen him or numerous opportunities to check or notice contrasted with zero sightings
I was here all day (or I looked for him many times) but in all that long period (or on all those many occasions) I didn't see him even once.
It may be grammatical but it is a sentence that makes one stumble. One reads "I never saw him" and is astonished to find it limited to "yesterday". Then one reads the sentence again to understand how you think, but it is an unusual formulation. "Never" is used without any limitation as in "He left and we never saw him again".
The normal way of saying it would be: I didn't see him yesterday.
'Never' puts an emphasis on the statement.
In the affirmative sentences we use 'did' to emphasise on what you are saying.
- I did see him at the party yesterday.
Here you affirmatively emphasized your point.
But what if in the same situation you want to say you didn't see him there. Then it'd be,
- I didn't see him at the party yesterday. (Here 'didn't' does not denote any emphasis on the statement. it is just a plain negative statement)
But what if when you want to emphasize the point that you did not see him at the party ?
So in these situations 'never' can be used
So you can say
I never saw him at the party yesterday.
So the meaning you quoted in your answer sounds correct to me.
I was waiting for him outside the office. But he didn't come.
I was waiting for him outside the office. But he never came.
(AmE) Normally I would use "never saw" if there was an extended or repeated window when I might have seen someone or something.
Rick Astley used to play at a bar by my house each and every Wednesday, but I never saw him. Now he is retired.
I lived in the Himalayas for twenty years. People said there was a yeti nearby, but I never saw him.
These concepts could apply to yesterday too.
The mailman normally drives by my house at 5. I waited and waited, but I never saw him yesterday.
Everytime I hear a bird sing I jump to my window to try to catch a glimpse of the oriole. Usually I catch a glimpse, but I never saw him yesterday.
People do occasionally use never saw simply to impart emphasis, but with a specific time in mind (e.g. "Accuse me all you want, but I never saw him at six o'clock last night" ) I don't, and it always sounds antiquated or uneducated to my ear. I think it is a matter of style, though, not grammar.