If you don't want to invest in a table saw, get precut laminate boards. Like the ones you'd make furniture from, Egger, Swiss Krono, Kronospan. There are wholesalers you can give measurements to and they will deliver finished pieces.

Measure out the box pieces, bear in mind boards have their thickness, usually 18mm, add additional internal piece the case will be sitting on. You can attach small rollers or just plastic nubs for sliding. Or get an entire drawer mechanism but that's additional cost.
You're going to need a drill, wood screws, drills for wood, ideally a clamp that allows to hold 2 boards at a 90 degree angle. A holesaw attachement for your drill, to make a hole for cables. The front seems to be held by magnets alone, you could order the front piece with hinge holes pre-drilled in it and add hinges.
Alternatively look for a website that lets you confiigure furniture and order a cabinet to spec.