It is not ambiguous at all. The phrase denotes that there is a purposeful, artistic, competitive way the game of basketball is intended to be played at all levels.
If you are not playing basketball for a purpose, don't bother.
The artistic piece is individual talent combined into a team concept and Geno describes this best as being like a jazz band, where the individual instruments often will get time to display brilliant solos but these solo must still fit within a team (band) framework-otherwise it is just another solo no matter how brilliant.
Similar to the purpose the game of basketball is competitive at all levels and demands that you do your very best at all times while playing. This is where IMO this player violated the "purity" of the game because the game demands that you try and make every shot.
Ok. Now I'll try.
The missed FT was purposeful and intended to have a predictable outcome. As far as I am concerned, under the circumstances it was within the spirit of the game, sporting, honorable, and
far more important than merely breaking a record. That moment made everyone who witnessed it better, even if only in some small, incomplete way.
As for "artistic" . . . what you describe as individual talent combined into a team concept (like a jazz band) becomes a less effective metaphor and conceptual framework when taking given isolated moments during the game. It is difficult to imagine anything particularly "artistic" in
this sense in standing at the line shooting a FT (this is
not to say that the manner in which a player may
shoot a FT is not aesthetically pleasing to watch; but that is not what I take the description to mean).
As for the "competitive way the game of basketball is intended to be played" . . . I don't accept that characterization if it is intended to foreclose upon moments like the one at issue, or for that matter other moments. I mean, UConn almost always dribbles out the final seconds of a game firmly in hand (opting to
not "try and make every shot"). Those final 10 seconds plainly cannot satisfy the "competitiveness" standard proposed. So, either the team regularly violates the "purity of the way the game is played", or (more likely) there is something incomplete with the definition.