You can't do that, only the Mac Pro can do that. The only reason the Mac Pro can get away with it is because its original unsupported GPU can be popped out and replaced with one that has drivers in 10.8. There is no GMA950/X3100 64-bit driver. You're SOL for running Mountain Lion on that machine, give up now.

Supports only 64 bit CPUs.

Supports only 64-bit CPUs and EFI of a flavor that (while I don't remember the technical details) rules out some early 64-bit Macs.

So, Hacintosh. Any good reason for this limitation?

I suspect the good reason is they didn't want to spend time making the 64-bit kernel support 32-bit EFI and didn't want to create and qualify an EFI update for 64-bit machines that have 32-bit EFI. Likewise, they probably didn't want to spend time supporting a 32-bit kernel when they stopped shipping machines which require it 5-6 years ago.

I think the only Mac shipped with a 32 bit x86 processor was the original 15-inch MacBook Pro. But I suspect the Intel GMA GPU may also play a part. I read the HCL and couldn't find a machine with anything less than an Nvidia chip.

Anyway, 6 years is a long life for a laptop.

Actually, many generations of Macs shipped with 32-bit processors. The first two generations of Intel 15" and 17" laptops, the first generation (at least) of Intel iMacs, and I believe three generations of Intel Mac Minis.