To me, ear training is any exercise which improves your listening skills. But also when I studied music in college it meant practicing both identification and sight-singing of intervals, chords, and melodies. However you go about it, it's about improving your ability to hear what's happening in a song, I think.

As a guitarist myself, I also think the "geometry" of learning chord and scale shapes is extremely valid and probably the best way to think about things. Our instrument has notes laid out on a grid and we can and should take advantage of that by thinking about things in a way that pianists and horn players can't!

I found that I was able to get a lot better just by learning multiple shapes on different parts of the need or with roots on different strings. (For example, if you learn e-minor pentatonic on the open string / 12th fret, that is a great too. But if you also learn it on the 9th fret with the root on the A string, now you've got a tool that covers the majority of the neck.)

And when it comes to reading... Reading music takes many forms: standard sheet music notation, guitar tabs, lead sheets, MIDI, etc. ALL of these are imperfect and imprecise formats for notating music that gloss over the nuances found in real performances to some degree.

A lot of intermediate classical musicians seem to fall into the trap of thinking that the sheet music IS the music itself (in the case of MIDI it can be, somewhat), instead of being an additional tool for learning and remembering musical ideas. Written music is imperfect.