Nope, it's not only x86 but requires an IBM PC/XT/AT compatible BIOS, so I don't think it could even run on non-PC compatible x86 systems such as the original Xbox or the current one.
Interesting trivia: the FreeDOS Kernel used to run on m68k machines. Pat Villani wrote a DOS-like kernel for m68k that simplified his embedded development at the time. Later, the kernel became Intel-only.
These days, the FreeDOS Kernel can only run on an Intel PC with BIOS.
You can likely make a 64bit DOS, or a flat-memory 32bit native one - at least one such one exists, it's just that no existing software will run.
We had this same discussion in the FreeDOS mailing lists as we decided what the next version after "1.1" should be. Some wanted the new FreeDOS to be 32-bit. I didn't go that far, but for a while I thought we should imagine what "DOS" would look like today if Microsoft hadn't killed MS-DOS when they moved to Windows. And it's an interesting thought experiment.
A modern DOS would have to update its memory model. DOS uses a segmented memory model, which made sense when the PC was a simple computing device. With the Intel 80386 processor, you could have multitasking. That's why Linux was originally written for the '386. So a modern DOS would also support multitasking. At some point, though, this modern DOS will break backwards compatibility with legacy DOS applications. To preserve some method of compatibility, we reasoned, a modern DOS would likely include a sandbox (like DOSEmu) to run these legacy applications.
But when you look at it, we already have that modern DOS. That's Linux. Because Linux supports multitasking, it has a flat memory model, it does all these other things. And if you want to run legacy DOS applications, you boot FreeDOS in a PC emulator like DOSEmu. That's not DOS. FreeDOS is still DOS, and needs to remain DOS. So we agreed the next version after FreeDOS 1.1 would be an update to FreeDOS. That's why this version is FreeDOS 1.2.