Is there a 64bit version of ubuntu for intel CPUs?

Yes, there is a 64-bit daily build of Ubuntu Raring Ringtail (soon to be Ubuntu 13.04) for Intel cpus. In fact, you mentioned it: it's the one that is called "64-bit PC (AMD64) desktop image". Yep, that's a confusing name and I'm sure it's called problems in the past, but that's the right one. (There's some sort of history behind the name, but it is correct.) It's the one I'm using with my 64-bit Intel cpu and it works perfectly. Download and use it with confidence with your Intel cpu.

"64-bit PC (AMD64) desktop image" is also for Intel's platform.

AMD64 is just the name of the instructions, and AMD and Intel processors are both able to understand them.

While the 64-bit PC image says AMD64 it does not mean it is only for AMD CPUs. This is the architecture description because the AMD64 instruction set became the prevailing instruction set for 64-bit consumer CPUs based on the x86 platform.