Well, there once was a chip called 8086, with a cheaper version called 8088 that was used in a personal computer called IBM PC. An improved version of that chip was made and called 80186, though that wasn't a very popular version. However, an improved improved version was then made, and called 80286. Now, that was a very popular chip, in particular because it was used in a computer called IBM PC AT.
Later, Intel, which created and sold the 8086, 8088, 80186 and 80286 chips, all of which had a 16 bits architecture, saw the need to create a 32 bits chip to compete with similar offerings by others. To take advantage of its incumbent position, it made the new chip capable of running software made for the previously mentioned chips. Naturally, Intel called this new chip the 80386.
Now, by this time there were lots of computers using various versions of the Intel chips, and there were also non-Intel chips that were compatible with the Intel ones. So people started referring to them as 80x86.
After a while, Intel launched a new chip, but it decided to drop the 80, so it became the 486 instead of 80486. Likewise, people was dropping the "80" from the front of "80x86", and calling this stuff just x86.
Now, I'm pretty sure some will come and say Intel branded their chips x86 at such and such time, which they did, but I don't care.
The fact is that the ever-increasing middle digit gave rise to 80x86, and x86 came from that -- even if 80186 and 80286 were not 32 bits.
So, once Intel finally went 64 bits, what did it call its new architecture? Right! IA64! :-) It also retroactively renamed the x86 to IA32, so to speak. Only IA64 was not compatible with x86, I mean, IA32, so everyone ignored it.
And then came AMD, which decided the market wanted a 64 bits CPU that was compatible, to the extent possible, with the x86 family. As a marketing appeal, they called it the "x86-64" family, and they were hugely succesful. So much so that Intel ended up grudgingly following with their own 64 bits CPU based on x86.
Later, because people are lazy, the x86-64 because known simply as the x64.
So, in answer to your question, because x64 is shorter than x86-64.