A setup like I have would work quite well for this IF you're willing to do a little tweaking and put some time into it. You can get it up and running fairly quickly but the more time you're willing to put in the more you can get out of it.
A small computer with an Ion chipset will be easily capable of playing back blurays and will be fairly light on the wallet and electricity. I chose to go w/o a NAS because having the computer on all the time takes no more power than a reasonable NAS would and now I have only one device I had to purchase.
Adobe does have hardware acceleration built into flash [an ion system has a very slow processor but a decent graphics card that is capable of decoding video] but I find that it is a little flaky. This means that web based videos usually work just fine, but sometimes do not. For instance amazon prime from their website USUALLY works but sometimes the hardware acceleration decides to die and the video gets choppy. That said the media software I use [XBMC] has a plugin for amazon that works 100% of the time. {I'll talk about software later}
An ion system would be capable of MAME.....my origional xbox is capable of running MAME, not the most demanding of tasks.
For an OTA tuner, I strongly recommend an HDHomerun from silicon dust. I used one before I got a DVR from the cable company and it was flawless. For software at the time, the only thing i found that worked decently was windows media center, which i wasn't fond of. XBMC is currently about to release a beta that has some PVR support.
For a second room you have a few options, and IMO there are two questions that sum up the direction you go for the second room, if you do a setup similar to mine. How much time, and how much money? If you're willing to throw money at it, a second computer is the best solution. Two of my rooms have full computers. My media library is centrally served and is displays identically between these two screens, including showing what movies/shows i've watched and it saves a bookmark for where i left off in a show so i can pick it up on any computer running xbmc. My third screen cost a significant amount less but takes a little more doing. I'm running a raspberry pi [a very inexpensive, very small ARM based computer] with a modified version of XBMC on it. Currently it doesn't have access to the central library, but it does have access to the shared media and can still play all of it, just less fancy about it. It also will work for amazon streaming, but will not let you access websites.
The other way to go is to get a dedicated media playing settop box (STB), like a WDTV live or one of popcorn hour's offerings. I have very little experience with these so hopefully someone else will give some more info. If you do like i do and have your media on an HTPC that you use as a server, you could use the STB to access that server in the second room. You could also go with a NAS in the closet and a STB on all screens, but I find that I enjoy the flexibility of an HTPC.
I hope these ramblings on hardware make some sense, I was trying to throw as much in as I could.
Here are some examples of ion based computers
Amazon.com: ZOTAC ZBOX Intel Atom D525 1.8 GHz Dual Core Barebone Mini-PC ZBOX-ID41-U: Electronics
Newegg.com - ASUS Eee Box EB1501P-B016E Nettop Intel Atom D525(1.80GHz) 2GB DDR3 320GB HDD Capacity Next-generation NVIDIA ION graphics Windows 7 Home Premium 64-bit