GoDaddy are a host, not the site police. They dont care if the people running the site have a broken form (unless its their server causing the breakage) and they dont care if the people running the site dont answer their emails. They only care if they pay their hosting fees, and arent hosting something illegal.
If it’s Personally Identifiable Information and you live in a country that enforces some form of privacy law that requires compliance, maybe. If it’s not, or you dont, then… no, they arent.
You’d have to contact the relevant national complaint authority if you have one. If you dont, you… move on with your life?
It seems like you’re dealing with a real issue, not spam. If the form is broken and emails aren’t getting a response, your best option is to keep following up with support. Additionally, try manually searching for your listing and look for a removal option. If those methods don’t work, you could consider filing a formal privacy request. Stay persistent, and hopefully, you’ll get a response soon!
Although these have been weeks where a lot of businesses are on low staffing levels, and maybe the people who can actually help you aren’t in the office.
But at the moment, you don’t know that your emails haven’t got through, only that they haven’t yet been responded to, which might be because of the season. Many places here only got back to fully open from yesterday, and will have a backlog of things to deal with. I’m not making excuses for them, I don’t know if any of this applies to them, or whether they’re just ignorant.
In any case, we’re back to the comments by @m_hutley earlier in the thread - there’s little that anyone here can do to help you.