The reduced non-finite clause

[Jededly]

Hello,Alan! Thank you for your help:-).
The people who win the game will receive this prize.
Because he didn't have free time he couldn't say "goodbye".
Could you tell me please if it is correct to call the clauses "having no free time" and "winning the game" the reduced clauses?
The people winning the game will receive this prize.
Having no free time he couldn't say "goodbye".
As far as I know the reuced non-finite clause is a clause that is the part of the full clause.
For example, "standing near the car" in "The man who was standing near the car was holding the newspaper"

[Alan]

Yes, the term 'reduced (nonfinite) clauses' is frequently used, although some prefer the more traditional label 'participle phrase'.