Mounting mirrored bathroom cabinet to plasterboard wall without usable stud
The manufacturer's instructions probably just want to warn you against using plain screws in plasterboard, which isn't strong at all.   

I have not seen or used the anchor linked in the question, but have used similar hardware to wall mount much heavier things to drywall.  Even adding weight for the contents of the cabinet, a single anchor will carry considerably more.  With four anchors, you're only using a fraction of the rated capacity.  

Since there's an electrical connection involved, to be extra safe, I'd locate the studs - there should be a stud somewhere behind the cabinet - and drill a couple new holes in the back of the cabinet to attach to the stud with screws.  It's really not important that the stud is not centered  on the cabinet.