No it doesn’t, yet another poorly written article. But the assumption can be made, as a quick google shows that in many places, public urination in fact gets you sex offender status. The reason is public urination categorized as “indecent exposure” rather than what it should be (something along the lines of disorderly conduct).
It is of course ridiculous but it seems that so many laws are not written to actually serve the purpose for which they are ostensibly passed, but to perpetuate a sense that someone somewhere is “doing something” about something that someone somewhere doesn’t like.
He has two previous Sex Crime convictions, and not for peeing in public, and he wasn't an 18yo teenager when he was found guilty of his first sex offense.