There's no inc equivalent for xmm regs, and there's no immediate-operand form of paddw (so there's no equivalent to add eax, 1 either).
paddw (and other element sizes) are only available with xmm/m128 source operands. So if you want to increment one element of a vector, you need to load a constant from memory, or generate it on the fly.
e.g. the cheapest way to increment all elements of xmm0 is:
; outside the loop
pcmpeqw xmm1,xmm1 # xmm1 = all-ones = -1
; inside the loop
psubw xmm0, xmm1 ; xmm0 -= -1 (in each element). i.e. xmm0++
Or
paddw xmm0, [ones] ; where ones is a static constant.
Probably only a good idea to load the constant from memory if it takes more than maybe two instructions to construct the constant, or if register pressure is a problem.
If you want to construct a constant to increment only the low 32bit element, for example, you might use byte-shift to zero the other elements:
; hoisted out of the loop
pcmpeqw xmm1,xmm1 # xmm1 = all-ones = -1
psrldq xmm1, 12 # xmm1 = [ 0 0 0 -1 ]
; in the loop
psubd xmm0, xmm1
If your attempt was supposed to increment just the low 16bit element in xmm2, then yes, it was a stupid attempt. IDK what you're doing storing into [rbx+8] and then loading into xmm1 (zeroing the high 96 bits).
Here's how to write the xmm -> gp -> xmm round trip in a less dumb way. (Still terrible compared to paddw with a vector constant).
# don't push/pop. Instead, pick a register you can clobber without saving/restoring
movd edx, xmm2 # this is the cheapest way to get the low 16. It doesn't matter that we also get the element 1 as garbage in the high half of edx
inc edx # we only care about dx, but this is still the most efficient instruction
pinsrw xmm2, edx, 0 # normally you'd just use movd again, but we actually want to merge with the old contents.
If you wanted to work with elements other than 16bit, you'd either use SSE4.1 pinsrb/d/q, or you'd use movd and shuffles.
See Agner Fog's Optimize Assembly guide for more good tips on how to use SSE vectors. Also other links in the x86 tag wiki.