To answer: Brazil can't specifically enforce what it asked for. Brazil isn't demanding the entire website to be blocked, it is demanding certain users to be blocked. This can only be done at the website level (nobody is gonna build a "Great Firewall" just for this).

What a court in Brazil can do in case of a "no", is then block the whole website, often done in simple ways (DNS) at local ISPs. It can also put the burden on local representatives of Rumble in Brazil, as it did with Facebook in the past (this means jail time for not complying with a court order).

In theory some people below mentioned that it can also forbid local Brazilian entities from performing commerce with the entity (like eg: fining advertisers paying for ads, or the advertise), but I'm not sure how that would work, since I'm not a lawyer.

Ok, thanks, I too was looking for this answer. What is the logic in voluntarily shutting down? Simply to preempt a ruling that would bar them from operating? Additionally, it would help stop the potential for action against Brazilian individuals and businesses who I guess could use a VPN which would be a gray area currently?

I can only speculate. Trying to get publicity? Wanting to comply with the court order without censoring individual streamers? Just moving away from a problem? No idea.