Given the social status of the crime, I think that accusing someone of grooming children is specific enough unless it's explicitly stated that it's not referring to the usual meaning, i.e. sexually.
No, grooming can mean things other than that crime and it is used in that context frequently on social media re: LGBTQ ideological indoctrination, you're perhaps just unaware of that.
Besides that implying someone has committed a crime isn't in itself necessarily a crime so your justification here is shaky, he was charged with malicious communications because the messages were deemed to be grossly offensive. The same act used here was also used to charge and subsequently fine the YouTuber who, for a joke video, turned his girlfriend's Pug into a "Nazi"... as that was deemed to be offensive too.
Re: your accusing someone of a crime angle, think about it, say there are some shifty-looking guys always parked on your road, playing music etc. you post on a local FB group having a rant about them, saying the police should search their vehicles... Have you accused them of a specific crime? Nope, you could be implying drugs, weapons etc. and indeed doing so isn't a criminal offense. You're just saying they're suspicious and the police should check.
Likewise, re: saying some parents should have their phones checked, he could be implying a few things there (you added one but he didn't say that)... but again that's also moot as suggesting someone is suspicious or worthy of investigation isn't in itself a crime anyway. (There are civil remedies for slander and defamation if necessary.)
The crime here was causing offense and that's highly dubious w.r.t freedom of speech.