I am studying some jazz piano licks and there are these inversions/variations and trying to understand how this is considered a Gm7 chords. There is no G in the chords and C which is not in a Gm7 but is in a Gm11. Why not call it a Gm11? Is this just an extremely loose definition? Or is just because if you take all the notes there mostly found in a Gm7? but still why not call it a Gm11? or G11?
Gm7 is the overall harmony, but the lick itself incorporates a Dm7 chord. The point of the example is to show a possible lick that will work with a Gm7 chord, even though it happens to use notes not part of the chord itself.
Put another way, the Gm7 is not labelling the notes themselves; it's labelling the underlying harmony over which the notes are played.
It's often a good move to use a chord tone on an emphasised beat in a bar. That way, even without the underlying harmony being played, the listener can 'map' where in the song you are.
There's no note at the beginning, which is usually the most emphasised beat in a bar, so obviously no chord tone there. However, at the next most emphasised place - beat 3, there is a chord tone, which goes on to spell a Gm triad backwards.
True, the chord could have been marked as Gm11, or Gm9, and some players would indeed play it as such. But I think the objective here is not concentrated on the chord as much as on notes which would work with the chord, in this case happening to be a more simple Gm7. It's not unusual that notes other than chord tones are used over any chord. In fact, in Jazz at least, it's not unusual for any of the 12 notes (which include chromatics) to be used over any chord. The author here decided those were what he felt would do a good job in this situation. Although what preceded and what followed would, to me, have an important bearing on what notes would constitute a phrase over Gm7 somewhere in a song. But we must have a choice of hundreds if not thousands of note combinations which would work over Gm7. That's only one of them. If it's from an educational tome, the author really should have included some sort of explanation.