Usually the size of general purpose registers is what defines the bitness of a CPU, not anything else (how much memory it can address, data bus width, etc).
For instance, the 80386SX was considered a 32-bit CPU because its primary register set is 32-bit, despite the fact it had a 24-bit external address bus and a 16-bit external data bus (32-bit requests are split into two 16-bit requests, this was done to allow the chip to be used on cheaper motherboards such as those initially designed with the 80286 in mind).
Note that this is for general purpose registers only: a chip may have 80-bit floating point registers in its FPU parts (supporting floating point with a 64-bit mantissa) but that doesn't make it an 80-bit chip. That was a bit more obvious when FPUs where external add-ons like the 8087 (the co-pro for the 16-bit 8086 family back in the day, which like current FPUs read & wrote IEEE754 standard 32- & 64- bit format floats and computed/held intermediate results in an extended 80-bit format).