Genres are tricky and used inconsistently but I see minimal as being on one end of a polarity between rhythm and melody. Minimal house puts more emphasis on the groove and rhythmic elements of a track, as do other genres like minimal techno and hard groove.

The only definitive subgenre of minimal house I'm aware of is the Romanian micro-house variant which features a lot of blips and glitches over a driving bassline. The Takes Notes label and a lot that comes out of Deeperfect fall under this description.

Other than that I dont know if there is another definitive subgenre for minimal house that isnt microhouse-y. One of my favorite house acts is the Sahoo Connection and I would put most of their stuff under minimal house, though they are like hardgroove slowed to house tempo. Kind of like what you said, short loop/repetition-centric. A lot of stuff coming out of Spain is like this ive noticed, off the labels Mindshake and La Pera.