Thanks - I would probably put something together with individual parts, as I already did back when we needed to connect PCs to our not so flat TVs via VGA, Component or SCART Adapters. However that box you linked to has a nice form factor and price tag. Not a fan of the Sci-Fi design though, but I just looked for some cases and there's some good stuff available - seems like a performant and A/V-receiver-seized PC is easy to pull off.
I used this case for my buildout. It's small, but supports full-size graphics cards and multiple internal hard drive bays. It's more or-less invisible on my bookshelf next to other components. It also doesn't have any drive bays, which looks very sleek and I just download everything from Steam (or similar) these days anyway.
Yes, that's exactly what I already had in mind. To be honest until yesterday I didn't even realize that Mini-ITX could handle the newer sockels and a decent PCIe graphic card. But with knowing that, this is a very good alternative to a console.