Yeah some people mount them by building an angled shelf (sometimes flat if it's a high cabinet) and using straps or large cable ties joined together. Try not to block the vents of the plastic casing, and make sure there's good ventilation in the cabinet itself, with fans if possible. The shelf needs to be quite strong obviously because of the weight, some people use metal brackets with lots of little screws, some people use wood with lots of very strong builders adhesive and nails/screws.
I've only ever mounted a genuine arcade monitor, which has it's own mounting bolt holes that fit right into the old cabinet I refurbished, so I've never had to build a shelf, so someone who has done this themselves might be able to give you more details.