I'm ... wary of how traveling is considered to be part of the crime(s).

He was charged under 18 USC subsection 2423(b), Travel with intent to engage in illicit sexual conduct, which pretty specifically makes it illegal for Americans to travel to foreign countries to have sex with minors.

It was travel to commit a crime on foreign soil against someone who wasn’t a U.S. citizen. The charge is a means by which his own government can still hold him accountable for a horrendous act.