That instruction was only introduced with the 80287. Unlike the 8086/8088, the 286 CPU was aware of different classes of x87 opcodes: it had to distinguish between ones that read or write memory, and some special control instructions as well.

So FSTSW AX was handled by the CPU microcode, which would read the status word from a reserved I/O port and put it into AX.

The 386 was even more tightly integrated, with some of the FPU state duplicated inside the CPU, so that it could store it to memory in different formats depending on whether it was currently in 16- or 32-bit mode.