How would I remove this table/cabinet?

It is probably screwed to the floor from inside the bottom of the cabinet so you should be able to locate those screws for removal. Normally the screws mounting to the wall come in from the opposite side before the skin is applied. If it were me I would try to remove as many screws as I could find mounting it to the floor. I'd use a magnetic stud finder to locate the screws along the wall. Then I'd hold a wide flexible putty knife against the wall as a shield to keep from marring the wall at each screw location as I used an oscillating saw with a thin blade to cut each screw. Then I'd use this technique to remove any remaining screws mounting it to the floor.