In 2005 you could already buy Intel processors with AMD64. It just wasn't called AMD64 or Intel64; it was called EM64T. During that era running 64-bit Windows was rare but running 64-bit Linux was pretty commonplace, at least amongst my circle of friends. Some Linux distributions even had an installer that told the user they were about to install 32-bit Linux on a computer capable of running 64-bit Linux (perhaps YaST?).

AMD was a no-brainer in the mid 2000s if you were running Linux. It was typically cheaper than Intel, lower power consumption (= less heat, less fan noise), had 64bit so you could run more memory, and dual core support was more widespread. Linux was easily able to take advantage of all of these, were as for Windows it was trickier.