He could release images, without him (Muyeol) showing up in any way, in an online forum and stuff, and do it in a way that can't be traced back to him. When people really want to harm you, they find a way to do so and he has the means... but I think, Muyeol unable to do that to Chani is how the author says that 'Muyeol is not that bad of a person'.... when even the suggestion is pretty bad itself. Apart from everything he has done to both protagonists.
Also Chani saying he somehow trust him, to no spread gossip and being like you said all bark and no bite is... really naive? And stupid too.
I really don't get his purpose more than being the antagonist. He's pretty unlikeable.
The thing is. He doesn't want to hurt Chani. He wants to own him. Probably be his lover or something. It’s a twisted kind of love and possessiveness. I doubt actually doing what he’s blackmailing Chani for would make Chani want to be with him. Its all just empty threats.
Also, for a person who is as famous as him, he wouldn't want to get tangled up in shady business like publicly shaming Chani. He does his thing in the dark.
If he releases the “pictures” as you say, dont you Chani will retaliate too? He wouldnt want that. His name and quite frankly his income is at stake
Of course, the scenario I was talking about was just in the hypothetical case that Muyeol really wanted to harm him. But like Chani said, Muyeol is not doing that not matter what he says, whatever reasons he has. I doubt he even likes Chani or wants to have a 'proper relationship' with him. Probably sees Chani as a challenge or a prize, and he likes the 'hunting' like the predator he is.
It's like you said, it's all about ownership and there many things that are still to be told about Muyeol. Chani doesn't like him. Period. Not one bit. But Muyeol's obsessive behavior towards those who leave or don't want to stay beside him must have an orign, more than being the rapist persistent asshole. At least Chani's dialogue about the manager being innocent and naive made it seen that Muyeol has a past. But rn who cares about him...

That’s a pretty dumb thing to blackmail anyone with.
“Yechan’s dick is gone, he has a pussy now!!”
Who could even confirm that? It’s not like people can pull his pants down in public. Even if he is scared, he can just have SeokJun to cum in him to get his dick back.
A better blackmail material for YeChan is to spread that you’re a fuck-ass molester