Ultra-compact, relatively powerful PCs are a dime a dozen. But when it comes to video editing, you usually need a dedicated graphics card (GPU), which accelerates the codecs and video effects.
Although many current processors also have integrated GPUs, these usually do not reach the performance of the smallest dedicated models. At the latest with 4K processing, work without an additional GPU usually becomes very cumbersome.
If you are still looking for a miniaturized PC for video editing, you might warm to the H31G from Minisforum. According to the manufacturer, this is currently the smallest PC with a dedicated graphics card. The additionally installed Nvidia GeForce GTX 1050 Ti 4GB naturally requires a corresponding cooling concept, which is realized via active cooling with heat pipes. Nevertheless it is possible to accommodate all components 15.3 x 15.4 x 6.2 cm.
As main processor either an Intel Core i5-9500F or an Intel Core i7-9700H can be ordered. In addition there are (not soldered and therefore expandable) 16 GB and a 256 GB SSD. The small model costs 659 dollars and the large version 799 dollars.
If you are looking for such a compact technology, you should also consider that similar components are usually built into laptops and can be purchased for much less. And then there is even display, keyboard, mouse and emergency power supply (battery) for free ;)