Not really, as paying for sex with a minor would be considered abusive. Also, it never claims she actually accepted the money. Also, if it happened in New York, the age of consent is 17 (although it doesn't say how old she was when the sex happened, only that she was 16 when she was contacted 6 months earlier)
EDIT: Yeah reading it it's definitely a money grab. It talks about how Ryan did terrible things and how RT is responsible for it. It also stresses legal issues that aren't relevant (Texas laws for conduct not in Texas, her age at the time of first messaging and that she's under 18 and was 16 at the time, but doesn't mention her age when they actually had sex).
The only thing of merit in it seems to be offering the $300, but even then they just use that in support of RT being responsible for Ryan's behavior.
My guess is they filed the suit when they couldn't get RT to pay up, in a bid to cause embarrassment. On brief inspection there's not a lot of merit to it unless she was 16 at the time they actually met up (which they very conspicuously do not mention).
tl;dr "I fucked him and it made me feel bad, so his employer owes me money."
That said, it could still succeed with the right judge/jury that was feeling particularly mad at older married guys banging teenagers. It could probably be beaten with enough effort, but it's just gross enough a case that they can use it to force a settlement to make it go away.