Looking at the product itself, it looks like it barely squeezes the mini-HDMI externally as is, let alone then PCB/internal available space.
I don't think there is, in fact, room for a full HDMI port. Mini HDMI is a compromise, and everyone knows it. It wouldn't have been included if full size HDMI was feasible.
The formfactor is self-imposed though, they could have made the device a few mm wider to accommodate a full HDMI port, but then it wouldn't be nice and square. Form over function maybe.
The form factor is based on the Apple Watch screen they use, clearly.
Mini-HDMI is fine for this use though and can just move with the item so it's not like you need to buy many.
That’s what I do, the jetkvm has its “own” mini hdmi that follows it as I have moved it from different machines. Buying one cable wasn’t the end of the world (I was able to snag the jetkvm for $70 during its kickstarter and a $10 cord) and I use it constantly so it’s never collecting dust