Is this statement absolute or is there a way around this condition if accepting the prize and taking the flights awarded as part of the prize?
Hello and welcome @c4az57b !!
It would be helpful to have some contextual information in relation to this prize you are referring to. Can you please provide a link to the terms and conditions this snippet is from?
Cheers! 
It would mean what it says I imagine. And no. What’s so difficult to understand.
My guess is:
It could mean the flights that you win may not earn frequent flyer or airline miles/points.
But that’s just a guess as there are no prize of actual miles/points that I could see when i did a 5 second skim of the terms.