Mainly by ear, but referencing plays a big role in that process.
For example, just comparing the Joe Satriani mix you posted with the OP's mix on a decent studio speaker system should reveal some obvious overall frequency differences on a half-decent listening system. I think I referenced a Joe Bonnamassa track.
When I listen to a track and analyse it, it's 4 steps:
1. Listen through and mentally propose and take note of what the issues are.
2. Find a comparable pro reference mix, level-match it and compare side-by-side to the mix in question, switching back and forth.
3. Switch on a Frequency analyser and see if the analysis visually confirms the issues previously proposed.
4. Grab an eq, sweeping around the problem frequencies, and try to improve the track to better fall into line with the frequency response of the reference track(s). Usually, at this point, I'm also using the frequency analyser in tandem with the eq to flatten out the frequency response somewhat, while still allowing for the Equal Loudness Contours (Fletcher-Munson) response pattern of human hearing, as well as any natural frequency bumps caused by the arrangement/instrumentation.
So yes, mainly ears, but eyes also.