Predicative participle vs restrictive participle

The first is not very natural. If a participle has an associated adverbial phrase, it is nearly always a post-modifier.
"on the track" would be an adverb of location, and explain where the man was running.

The second is fine.

These are more natural examples of "running" as a pre-modifier:

Look at the sunlight reflected off the running water.
We have

Thank you very much Mr.AlpheccaStars for your concrete accounts.
If the speaker is telling of the only man running on the track, in #1, Could 'running' be used as the restrictive use to indicate a certain man?

Not really.

Here is an example of a restrictive clause:

The man running on the track is my cousin.

It implies that there are many men in the vicinity, but only one is on the track, and that one is my cousin.
You can tell if a clause is restrictive by taking it out of the sentence. If the meaning changes, the clause is restrictive.

The man is my c

Thank you for your concrete accounts^^
I see^^; your answer is very helpful for me.

park sang joonThank you very much Mr.AlpheccaStars

Please don't assume that AS must be male just because she always gives sound answers.

Oh! I didn't know;;
I am at a loss for words; I'm so sorry ??
Please pardon me.

park sang joonPlease pardon me.

That's alright. I've been called worse!

You are so generous; thank you Ms.AlpheccaStars.
It looks to me like your nickname cause a misunderstanding about your gender,
but l like your nickname^^

park sang joonIt looks to me like your nickname cause a misunderstanding about your gender,

In English, first names that end with the letter A are usually female. This doesn't always work for nicknames though. Aspara Gus is male (Gus is normally a male name).

I didn't know; thank you Mr.Blue Jay for your helpful information.