If you could give us a budget that would really help fella. I realise you are probably just putting "feelers" out to see what is possible for what price but if we knew the MAX you were willing to pay for everything that would help us help you.
That "steam box" isn't as well spec'd as the Trinity setup some of us have spec'd you. The H61 mobo lacks sataIII support (this matters as you may well add a SSD later), it only has 2 DIMM slots for RAM, which they have filled with 4GB of slow RAM. Basically they have built the rig around the 7770 GPU which as I have already said is pretty poor value for the price tag, with cheap parts to get the job done.
Myself and the more experienced members on the forum will nudge you towards the FM2 socket if you want to keep the price low as you can leave out the GPU and add one later when you want more grunt. Stulids video link showed that the Trinity APU can play what you want with the Spec I gave you.
That video link for the "steam box" i've seen posted a number of times here and I think it's misleading in that the £300 doesn't cover the OS. It's an option but I wouldn't recommend it personally. I did point out you can use the windows 8 preview edition for free but at some point you will have to pay for the OS.
I look forward to seeing your budget and what we can swing for you