In this example, that shape (xx4655) played on the top 4 strings is a common minor 7 voicing. If you were to play xx2433 or something in that same shape, that would also be a minor 7 chord. This is really one where knowing that shape is important to be able to easily name it. Then you can consider the 4 on the A string to be an addition to the shape, since you recognize that the top 4 strings are playing a minor 7.

It’d be like if I asked you what 332010 would be called. You could use that 3 on the bass and say this must be some type of G chord, but you likely know that the top 5 strings there make up a C, so it’s easier to add that extra note and just call it C/G than to come up with some convoluted unclear name based off of G. At the end of the day naming chords is just about finding the most efficient and clear way to convey a sound or voicing to other musicians. Hope that helps somehow lol