If it happened on the job then, yeah, they probably would. Just like there is a Walgreens security guard in the news currently for killing a shoplifter in SF. If he had killed someone outside his capacity as a Walgreens security guard, they wouldn't describe him as such.

If this engineer had killed themselves in another manner besides jumping off the top of their workplace, they might not be described as a Google engineer.

Edit to add: Statistically, I suspect that there have to have been many instances of Google employees committing suicide outside of work. I doubt those got headlines at all, let alone headlines including Google's name.