Jorg… are you using Steam on Linux?
No motivation to pay close to 1000 for a steam box, but an i3/i5 with Intel graphics would be ok price wise… question is, would it be worth it?

Short answer: Yno.
Long answer:

This is a question in multiple parts, namely:

1. Do you use Steam on Linux?
2. Does Steam on Linux work well?
3. Are integrated graphics sufficient these days for games?
4. What about graphics drivers?

Now, let start with the easy part: Yes, I use Steam on Linux.  I basically only use it on Linux and one of the main criteria for buying games on Steam, or from Humble Bundle, is Linux support.  Steam, the application, works very well on Linux and it comes down to installing a package and that’s it.  That said, Steam is just Steam, being a kind of game library with a useful “Big Screen” (aka, “use it on TV”) mode.  On no configuration, did Steam refuse to run, but nobody runs Steam to run Steam.  What you want are the games.

That’s where question #3 comes in, and sorry, no… Linux won’t compensate your underpowered hardware.  Just as in Windows, you might end up buying a game and figuring out that “hell, fuck no, this won’t work“.  If it’s not because the game doesn’t start up at all, it will be because it is so horribly slow, that it’s unplayable even when turning down all the settings.  Now, in all fairness, my experience with Steam on Intel, limits itself to:

• Zotac Nano ID61 – Celeron 867 / 8GB RAM / “Intel HD Graphics” (I have given this machine away, I can’t do tests any more)
• Dell XPS 15 – Core i7-2630QM / 16GB RAM / “Intel HD 3000” (Paired with an NVidia GT 525M)
• Acer Aspire S3 – Core i5-3317U / 4GB RAM / “Intel HD 4000”

All run Ubuntu 14.04LTS with Steam installed from the Valve repos.  These are all older chips based on Sandy Bridge (Celeron 867 and Core i7-2630QM) and Ivy Bridge (Core i5-3317U) architectures, so obviously it’s not very representative for modern Intel hardware.  Take everything I say with a huge grain of salt.  Haswell, Broadwell and Skylake based processors might be so much better, especially with the Iris Pro graphics.  Intel graphics are so very diverse and the labels stuck on them make it next to impossible to find accurate benchmarks.  So basically, what it means is that I must go on feeling which really, is very subjective.

However, it’s not the only thing you can go on.  You can simply see what the minimum requirements for some games say.  A very well known AAA type game working on Linux is Sid Meiers Civilisation V.  Go and visit it, and you’ll notice that in the PC world, you damn better do your homework about your hardware and what this hardware means in relation to recommended and minimum settings.  Also, keep in mind this is a strategy game, and really shouldn’t tax your graphics card all that much.  Well, go and look:

• Windows: Core i3 or better integrated graphics
• Mac OS X: “Intel GMA (950/X3100), HD 3000” not supported
• SteamOS/Linux: Intel Integrated video chipsets (GMA 9XX, HD 3XXX) will not run Civilization V for SteamOS and Linux, and are unsupported.

So, the Zotac is out as is the i7 (using Intel graphics).  The i5 might run it, I don’t think I tried.

Another one?  Let’s take Victor Vran.  I bought this game because the gameplay reminded me of the PlayStation 2 version of Baldurs Gate.  I didn’t check specifications and I tried on the i5-3317U, connected using HDMI to my TV.  The game loads, but it is unplayable at any detail level.  Specs, here you go:

• Windows: GeForce 8800 or higher, AMD Radeon HD 4000 or higher, Intel HD 4000 or higher (min. 512 MB VRAM)
•  Mac OS X: OpenGL 4.1 (GeForce 600 or higher, AMD Radeon 5000 or higher, Intel HD 4000 or higher)
• SteamOS/Linux: OpenGL 4.1 (GeForce 600 or higher, AMD Radeon 5000 or higher)

Hey!  Intel isn’t even supported on SteamOS/Linux.  I should try it on Windows to see how playable the game is, but I doubt it will be a very agreeable experience.

… you’ll notice that neither of these games is even a first person shooter-puzzler.
Indie games will work, right?  Right?

Yeah, kinda… Again better check what the specs are.  Rochard works fine, for example, and is a fun game.  Less graphically intensive games like World Of Goo or Thomas was alone work perfectly.  Rochard and Thomas was alone and are a joy to be played with an XBox controller, which works out of the box on Linux.  Are these your kind of games?  You’ll be happy with Integrated graphics and Steam.

However, not all is perfect. Which brings us to the drivers and question #4.

How are the drivers?  Intel has a good reputation on Linux for drivers, but, and that’s really a but… that’s because AMDs drivers are quite horrible and NVidias drivers are closed.

Are Intels drivers good?  Generally, yes, and it might just be because I use whatever comes stock with Ubuntu 14.04LTS that I have problems in some games.  Most of the issues here are in my i5-3317U (which is what I use for most casual gaming).  First time I noticed that something was wrong was that in certain scenes of Book of the unwritten tales – Critter Chronicles, the characters were very dark.  That’s a point ‘n click adventure, nothing graphically too fancy.  My guess, is that they used a badly implemented shader.  The game was playable, but when it happened, it looked ugly.
Recently I’ve been playing Never Alone, which is very playable on the i5 from a performance perspective.  However, the game uses some shader that is broken.  Probably the same issue as mentioned before, but it’s so much more annoying because the shaders move and look so very much out of place.  Is it playable?  Yes.  Is it pretty?  No.

There is also something strange going on with the i5.  Due to a flash of genius, I had the idea to just connect the laptop to my TV and play on the TV.  I set the TV as primary display and disabled the internal panel.  The surprise came when I tried playing something like Stanley Parable or Talos Principle.  They were unplayable, at any resolution.  Why is this remarkable?  Because I played these games on the Zotac ID61, which is immensely lower spec than that laptop.  Something is going, on, but I have no idea what.  Given these games play fine on the internal panel, my guess is it has something to do with the drivers and how a dual screen configuration is handled.

Back on topic: if you’re using Intel Integrated for gaming (within the range of chips I talked about), you get what you pay for.  I could recommend looking into AMD offerings, as their integrated graphics solutions are better, but you’ll still end up with disappointment.  I was rather happy with my A8-3850 (Radeon HD 6550D), but as a matter of fact, you’ll end up running most games on low settings any way.  I have given up and just got myself an low-range NVidia gaming card.  (Which I haven’t tested properly to tell whether it was a good idea.)

What does this mean?
Linux gaming will work, if you have the hardware to match.  If you don’t the experience will be as crappy or crappier than on Windows.  That 1100€ SteamBox suddenly does look more attractive, doesn’t it?   No, I don’t have that kind of money for toys either, but my fans can of course send me one as a present ;-).  Whether such a SteamBox will actually play games well enough, that, I cannot say.  Maybe consider a Steam Link to your real game box?