Possibly, the Apple Mac mini, Intel Nuc, and Nettops would be good for casual desktop PC gaming for casual PC gamers and non-gamers who mainly play flash games, web browser games like Minecraft, and play their games in low, medium, or medium-high video quality settings and low resolution video settings like 1024x768 or 800x600.
http://www.youtube.com/watch?v=o2ty1upTlXY
I saw a video of the Intel Haswell series of CPU, and Integrated GT3 video card running Grid 2 Racer on high settings, and it ran pretty smoothly, so when the Intel Haswell comes out for the Apple Mac Mini, Intel NUC, and nettops, they would make for good casual gaming pcs for people who mostly play older games, and games on low to medium high settings.
The Intel NUC and AMD LiveBox nettops will run the weakest possible graphics. You have posted the highest grade integrated graphics that Intel has to offer.
In fact, they won't even have up-to-date hardware.
The Intel NUC uses a Intel HD 4000 which is good enough for most flash games, older games like Warcraft 3, Counter Strike, and games made in the early 2000s till now if the maker of the games designed their games to run on low to medium video quality on Intel HD 4000 graphics chips which are found on the Nuc, Mac mini, and Surface Pro tablets by MS.
The Intel Nuc uses an Intel i3 Dual core 1.8GHz CPU, max memory up to 16GB of 1600 MHz DDR3 RAM. It also has 2 PCIe* mini slots (1 half-length & 1 full/half-length)
I notice a lot of PC gamers who don't play a lot of PC games seem to mainly play Minecraft, Runescape, and less intensive games based on YouTube comments, and online posts, and I think Minecraft can be played on slowers PCs like Nettops at higher video settings.
A lot of gamers seem to enjoy the classic versions of Counter Strike, and find newer Counter Strike games not as good because the community for CS is bigger than CS Source, and CS 1 can run on many computers even computers with slower parts. Plus, CS is the original Counter Strike.
I think Inexpensive smaller desktops like nettops would be great for people who enjoy playing games like Minecraft which are less intensive PC games, and games which have memorable gameplay like Warcraft 1-3, Starcraft 1-2, Diablo 1-2, The Sims, but are not very intensive when it comes to video quality.
A lot of popular RPG, RTS, and racing games can be played on an Intel HD 4000, or equivalent and slightly better graphics card.
I can speak from experience on the Mac mini, but I don't know about the other mini PCs. I own a fairly recent Mac mini, it's the second-to-latest model I believe. I could run Diablo 3 on it on regular settings (I think) and I ran the previous Tomb Raider, and I'm sure Minecraft would run just fine. I've used it for gaming a little because it's hooked to my TV, but I never stick with it. I built a gaming PC for around $450 that does way better and was cheaper than a Mac mini. While I love Macs in almost every other area of my uses for computers, they unfortunately still aren't the best bet for games, there is much less selection available for Mac. So unless you really just like the form factor of a Mac mini, the best bang for your buck would be to build a gaming PC. It's easier than you might think!
If you just want to play very old, Android or browser based flash games, sure they're a great option. However, any power user would suffer mightily on one of those things. It definitely would not be good for any sort of gaming, not even low to mid for that matter. I'd get those type of computers for someone who just was a very casual internet browser and needed it for word processing functions.
They also could be good for HD video playback since a lot of smaller desktops have better video cards like the Intel HD 4000, Nvidia GT 610, and AMD APU.
I probably get what is cheapest, and offer the most bang for the buck, or whatever is on Sale or can be bought cheaply at eBay, and Amazon.
The Intel Haswell Series of CPU, and integrated HD 5000 video cards are pretty good, so if they go in the Mac Mini, and Intel Nuc, the video performance should be about the same as a Macbook Air 2013 which uses the Haswell CPU, and HD5000 series of graphic cards.
