The shelf is 400x400mm with a 'through height' of about 250mm.
However, Due to the sloped back of the Vewlix you only have about 350mm of depth to play with. So your PC would just about fit in even if overhung a little horizontally but I think you might be a bit tight on the depth as you need to take into account the cables that plug into the back/front of the PC. Depending on the location of the fans in your PC you also might not want the front of the PC right up against the front door of the Vewlix. Obviously if you run the cab with the front and back door off you'll be ok but that might not be what you want.
I've been sorting out a couple of mini and micro atx systems for my two Vewlix's recently:
Neither are particular power houses but they're fine for what I'm running at the moment. I've had the PC in the Cooler Master case for a while and it fits in the Vewlixs lovely. The white Jonsbo C6 case was a recent pickup as I needed to transplant the guts from an older PC into it. The below Silverline case was a pretty small midi case (It used to fit in an Astro City) but it wouldn't fit in the Vewlix's.
I made life hard for myself by picking up a used RTX2060 which I didn't realise was a triple width GPU at the time. I had a real hard time finding a case that would fit inside a Vewlix but would take a triple width albeit short GPU and the Jonsbo C6 was one of the few that fit the bill.
Even though the case is perforated all over the airflow is meant to be pretty shit as the holes are so small. Luckily the panels pop on/off really nicely so I've been using it with most of the panels removed. As the case is quite compact there are not too many cooling options and I could only fit a 120mm fan on the front as stock so I made my own adapter plate to fit a 140mm.
I found out since I could get two 120mm fas on the front so that might be an option if I have issues, so far soo good though but I've not really been playing anything too demanding.
There's plenty of room around the case though:
For reference the Jonsbo C6 is 202 x 266 x 295.2 mm.
I'm planning on making some nicer plates/panels with better airflow for it in the future.