MIPS technologies is a lot more like ARM than it is like Intel, in that it licenses its architecture and designs to other companies that can then build chips on their MIPS architecture. MIPS hasn't had ARM's success in the mobile market so far, though. The MIPS chips right now are slightly weaker, and on an older processing node (65 nm last I checked), but they promise to be somewhat more energy efficient (about 30% more) and cheaper (although that could be because of the older manufacturing process).
So then what would AMD have to gain from buying them out? I think this would be a very interesting move for AMD. Even if AMD would adopt ARM right now, and start making ARM chips themselves, chances are that they are already too late in the game. Others like Qualcomm, TI, Nvidia and Samsung were years before in this, so they have more experience, and know how they can make the best of the best ARM chips right now. I'm not so sure if AMD as a new player can compete with them right out of the gate, although it's certainly not impossible.
However, I still think that buying MIPS makes a lot more sense for AMD. Why? Because adopting ARM means becoming just another ARM chip market, so competing with the established players head-on. That sort of strategy rarely works for a newcomer. The best strategy is to disrupt them with a new type of product, and change the rules of the game, so that you are put in the position of the leader, at least in certain areas.
If MIPS chips can be significantly more efficient and cheaper than ARM chips for the performance they offer, and that actually impacts the retail price of the device, then I could see how AMD could carve itself a nice niche market in the mobile market - like say for low-end sub-$100 phones and tablets. AMD could become popular chip maker then through the sheer volume of chips that they would be selling, and that would give them bragging rights for a pretty big share of the market.
Plus, while MIPS may be on an older manufacturing process right now, I believe AMD can help them be up to date on 28nm, or 20 nm in a couple of years, by the time they finish the merger and show their new chips. MIPS also has support for 64 bit, so they are ahead of ARM in that as well, but it might not matter by the time AMD pushes them into the market, because ARM will have a 64 bit architecture in 2014, too.
Now we know why it would make sense for AMD to buy them, but what about Google and ARM? What could they possibly do with it? I do believe Google wants to start making hardware itself, but I'm not sure why they would need an entire chip architecture for themselves. Perhaps they are thinking a lot into the future, where MIPS could become a sought architecture even by the likes of Apple and Microsoft, and that would give them an advantage then. But in the short term, ARM might not like it that Google is buying a competing architecture, although I'm not sure what they could do about it, because Android is currently the most popular OS for their ARM architecture.
Why would ARM buy it? Well, besides the engineering insights for the MIPS technology, they'd also get to eliminate a competing architecture from the market. Perhaps they wouldn't eliminate it for good, but it still means it won't compete with ARM anymore. This is also the option I'd like to see the least, because even though ARM is great at the moment, it would still be great if they had 2 other architectures to compete with, like x86 and MIPS.
My bet is that AMD will get it, unless Google really wants it. AMD can't outbid Google and neither can ARM. Either way, I'm looking forward to the outcome of this.