The article states that the loss is "only in some cells," so not a systemic issue. That may affect those tissues, but for it to be a "cause," it would need to be system-wide.
Even the transgender folks who come out late in life admit they had experiences, thoughts, and feelings when they were much younger. This suggests that the theory that "we are born this way" due to a divergence in brain/body development is more likely.
Possibly, the Loss of Y later in life exacerbates the already existing gender dysphoria, which then motivates us to finally do something about it. Later in life, we generally have more stable living conditions, maybe be retired with more time for reflection and introspection. I can see those being more of a factor than aging cell chromosomes.