720p gaming isn't all that taxing. I don't play any of the games you listed but you'll get plenty of pop out of an A8 with a 6570. I have an A4 with a 5570 that plays 1680X1050 with low/ medium res settings on a lot of games.
I assume you already have a motherboard. The 6570 would do hybrid-crossfire with that APU, but crossfire is usually more headache than it is worth.
Consider getting the A10-5700, it is the same wattage, but has a lot more GPU power than the A8-5500, only for a little more. Obviously I wouldn't get the 6570 anyways, so in the end it is cheaper.
The 212+evo is a good fan cooler, around the $30 you are asking, but I don't think it is really needed. Stick with the stock fan, if it isn't cool or it is too loud, then go ahead and get an aftermarket fan. This is just my opinion, and other people are likely to disagree.
Edit: The 212+evo is taller than the case is, so it won't work. (I also tweaked some wording) There aren't a huge number of low profile fans (well there are but most of them seem far too cheap to be worth it).
I tried my best to get something close to what you picked out, but I did change come things.
1st if the APU. I went for a stronger one and dropped the graphics card.
2nd is the RAM. This is higher quality, higher performance, higher capacity, and within 10% of the price.
3rd is the storage. You obviously plan to record TV to your hard drive. So I recommend getting at least 2TB, 1TB will fill up fast. I dropped the SSD, but if you must be able to load the OS fast, then re-add it, but that is more personal preference, and isn't going to affect your games (based on the ones you mentioned.)
4th is the sound card. Unless you are spending a lot more, a cheap sound card won't be any different than the onboard audio. Again, you can re-add it, but I assure you it will add nothing to your build but cost.
5th is the PSU. 80+ gold is overkill, so I am saving you a few dollars there.
Things are otherwise identical. This should make for a nice HTPC. Please let me know how things turn out.
P.S. There is nothing 'wrong' with your part choices, they would do what you are asking of them the same as the parts I put forth, but seeing as mine is a bit cheaper (I really hope I didn't forget something, that would be embarrassing), and you can still tweak a few dollars out of it (1TB instead of 2TB should save you $70.)
Watch out when using Dolphin and PCSX2 - They are EXTREMELY CPU heavy in terms of Clock speed and Single Thread performance.
I recommend going for an Intel CPU with a cheap GPU - Something like a Core i3 with a decent clock speed will keep PCSX2 running nicely (it only uses 2 threads), because the IPC on the Intel chips are much higher.
I have noticed that the trinity chips perform very well due to their high clock speeds though, the A10 - 5800K should outperform anything Intel based at the same price, mainly due to the IGP being so advanced.
tl r - Cheap Intel Chip (i3) + Cheap GPU = Good
- Cheap APU + Cheap GPU - Not so good
- Expensive APU with no discrete GPU - Good