but even then people who can't produce either can't be simply classified into what they were "supposed" to produce without involving karyotypes or other sex characteristics, which the paper you linked explicitly argues can't be used for sex definition:

Here I synthesize evolutionary and developmental evidence to demonstrate that sex is binary (i.e., there are only two sexes) in all anisogamous species and that males and females are defined universally by the type of gamete they have the biological function to produce—not by karyotypes, secondary sexual characteristics, or other correlates

so for someone with complete gonadal dysgenesis:

• they produce no gametes
• their sex is defined by... which gamete they have the "function to produce"
• we determine this function by... looking at their chromosomes (XY = male function, XX = female function) or other correlates

but then this is circular:

• if sex is defined by gamete function
• and gamete function can only be identified via determination mechanisms in non-gamete-producing cases
• then determination mechanisms are also doing the definitional work

and I feel your lacking-an-arm comment doesn't really apply here as humans aren't solely defined by how many arms we have - the analogy would only work if:

• sex were defined like humanity - as a cluster of traits with gametes being just one feature
• but the paper explicitly rejects that (arguing the monothethic model is the only true one when the polythetic clearly covers more cases)

but I think the bigger question this whole biological definition/determinism sidesteps is the one that seems close to heart of the very-same intersex people linked in that Wikipedia page:

Paradigms for care are still based on socio-cultural factors including expectations of "normality" and evidence in support of surgeries remains lacking.

"Nearly every parent" in the study reported pressure for their children to undergo surgery, and many reported misinformation.

The report calls for a ban on "surgical procedures that seek to alter the gonads, genitals, or internal sex organs of children with atypical sex characteristics too young to participate in the decision when those procedures both carry a meaningful risk of harm and can be safely deferred."

when these things affect human beings we can't try to wash our hands by clinging to models that seem to give us simple answers - if we insist on monothethic definitions that don't recognize the complexity of sexual development - we end up forcing ambiguous cases into boxes and providing intellectual cover to deny people agency over their own bodies.