Is there a fallacy for not letting the other side speak?

"So is there a fallacy for this kind of in-debate behaviour?"

This isn't "in debate behavior". Was there a pre-agreed-upon definition of terms? Was there an agreed-upon format? Etc.....

My point is "debating within viewpoints" on the internet is a discussion. Either person has the right to disengage for whatever reason they seem fit. Don't make the mistake of the non sequitur fallacy of concluding "they ceased to discuss therefore I 'won' the debate". They simply quit....that's not fallacious.

Not really. It's just refusal to engage. 

It's like the two of us having a debate, live on stage, and me walking off in the middle because it gets too heated. There's no error in reasoning here - just a person who might need to manage their emotions better. 

If their last response was a fallacious claim in response to your claim, and then blocked you then It could be an Avoiding the Issue Fallacy. 

It's more of a rhetorical technique most similarly referred to as the Gish Gallop. It's easier and faster to fling misinformation and doubt into an opponent's stance/position than the length of time and difficulty to correct said misinformation and doubt.

Unless they're using the rant itself as a further argument to support their side, it's technically not a fallacy as much as it is foul play.