These clues solve toA word comparing things = THAN
A neuter genitive = ITS
A noise that horses make = NEIGH
A bone supporting teeth = JAW
A light-ish purple hue = MAUVE
A path for
null= DEV [as in Unix /dev/null and /dev/full]
A thing that you can play = GAME
and the poem's meter and subject matter are a reference to the Sound of Music song "Do-Re-Mi", in which Julie Andrews teaches the von Trapp children about solfege with a series of helpful mnemonics (like "DO, a deer, a female deer" and "MI, a name I call myself).
If you sing the ditty with this variant solfege system, the tune is
ITS THAN NEIGH MAUVE GAME DEV JAW NEIGH THANwhich is to say,
IT'S THE NAME OF GAME DEV JONATHANwhich is BLOW.