What does this mean ?

 What does this message mean that I get after every game that I play ? "This game does not qualify for player league"

It is about the Players League where you can earn points and compete with others to get promoted to new level divisions. It's purely for-fun and does not have any impact on your chess rating.

Not all games can give you points for Players League.  So that message is popping up to tell you.

More about Players League: https://support.chess.com/article/2813-what-are-leagues-how-do-i-join-one

 So which games can give points for Players League because I have never encountered such a game ?

This official support article describes which games do and do not qualify for Leagues: https://support.chess.com/article/3176-i-just-won-a-game-why-didnt-i-get-any-league-trophies

I believe the site only recently implemented a message to be displayed for matches which do count towards League points.

Dear Team at Komodo help,

Further to my previous emails regarding Error message: "Assertion failed: (Score >= -32500) && (score <= 32500), file transposition.cpp line 148" It seems this is indicating that an internal inconsistency was detected by the code which was so serious that the program could not meaningfully continue. In this case, Dragon apparently retrieved a position evaluation from its transposition table and found that it was outside the range of +/- 32 pawns, which is apparently the maximum value that it would ever store. Probably the retrieved values was some random garbled memory due to a bug. Once you detect those kind of errors likely the play would be all messed up, so it just stops. I believe Dragon also crashes in other venues. (not sure of that) so there is no particular reason to suspect a flaw in my setup. It is disappointing that the software is so unreliable. Please could you respond to this query?

The above is in reference to continuous crashes with Dragon 2.61

I don't really need the help of the message as I can't catch up anyway with all the insomnicas.