Hello mrnonamer: Well... I don't know where you live. I also don't know anything about this website you visited. But, personally, I would have to say no, what your fiancé is doing certainly is not illegal... at least not in any practical sense.
Actually, there was an interesting article in our local newspaper recently that bore on this subject. Basically what it was saying was that "giving someone the silent treatment", so to speak, is a form of emotional abuse. So, in cases where a person doesn't feel able to talk through a situation right away, what the article suggested was that the person who does not feel ready to talk should clearly state this & ask for time to cool down... think things through, etc. From what you wrote, it sounds like this is what you've been doing. But instead of getting the space you need, you're meeting with anger & verbal abuse. Unfortunately, human nature being what it is, I doubt making a video of one of your arguments, & showing it to your fiancé, could be expected to result in any kind of positive outcome.
The problem here, from my perspective, is that you each have your own way of approaching dispute resolution. And neither of you seem to feel able (or perhaps willing) to adopt the other person's approach. In order to resolve this impasse, either one of you is going to have to give in & adopt the other person's approach, or somehow the two of you are going to have to find some compromise. Of course, the mainstream way of approaching something like this is via couples counseling. However, that requires that there be two willing participants, which there may not be in this case. That being the case, my suggestion here (having been married for over 30 years) would be, (to borrow a phrase from the old original "Star Wars" movie): "Let the Wookie win..."
I see this is your first post here on PC. So... welcome to PsychCentral… from the Skeezyks!

I hope you find the time you spend here to be of benefit.
PsychCentral is a great place to get information as well as support for mental health issues. There are many knowledgeable & caring members here. The more you post, & reply to other members’ posts, the more a part of the community you will become. Plus there are social groups you can join & chat rooms where you’ll be able to connect with other PC members in real time (once your first 5 posts have been reviewed & approved.) Lots of great stuff! So please keep posting!