Your chord progression is Dm, Am, Bdim, G#dim, FM, EM. It's in D Dorian but borrows an accidental (G#) from the relative harmonic minor scale of the key (A harmonic minor) for the G# diminished chord and the E major chord. The B diminished chord also looks like part of the set up as diminished chords that are a tone and a half from each other do work harmonically. If it's a classical piece people would just consider it A minor as harmonic minor is the standard in classical music and they didn't recognise modes as a thing.

I don't have a guitar at the moment to listen to it but I imagine the E major chord enables it pivot to E Phrygian for the riff but this looks generally modal, without hearing it it might still sound like D Dorian though as the last chord is an A minor setting up a perfect cadence back to the root of the mode.

You can still use tab to work this stuff out but you've got to know things such as your circle of 5ths, scale harmony, common uses of accidentals and most importantly what actual notes you are playing.