Maybe I can provide you with some clarity to what they really mean by unlimited.
Let me start out by telling you, the unlimited plan, is generally spoken about when it comes to their shared server accounts.
On a dedicated server at hostgator, there are between 200 to 400 shared accounts. I've actually seen almost 500 shared accounts on 1 dedi at one point. Moving on. They use a dedicated server, to serve as a shared server which hosts' all of those accounts.
The meaning of unlimited is limited by what the server can handle. Although, they do mean "unlimited". You can have as many domains as you like, as main websites as you like, databases, bandwidth, and etc..
however, you can only have that, if the server allows it. You are allotted a certain amount of nodes per shared server. Nodes are files.
each file equals 1 node. They say that you are allowed unlimited nodes, however, if the amount of nodes you have on the server are causing problems with the server and other accounts, then they will email and let you know about it, and ask that you do some clean up and remove some of the files.
AS for bandwidth goes, you are allowed unlimited bandwidth, but theres a catch, like always. The shared servers, allow for 25 simultaneous connections. Which means, you can only have 25 connections per domain at any given time. This doesn't mean that you can have only 25 people on your site at a time. this just means, that the connections are limited to 25. Example, Lets say that 100 people are viewing the main page of your site. None of them are connected to your site. The site gets loaded in their browser, then disconnects, but when interaction, or navigation, or any action occurs by the user, that invokes a connection to the server. Don't misinterpret that.
Disk space is unlimited, but they may ask that you remove some files if it becomes a problem as I said before. Also, they have automatic backups. Which only back a certain amount of files/nodes up.
If your nodes go over, and on the cpanel, you see that bar turn red. Dont worry, it just means that the most recent nodes will be backed up and nothing more.
Although, they were talking about changing it, so that the backups don't run if you are over the limit. That part is heresay for now though.
My personal opinion, I wouldn't run a video hosting site from a hostgator server for several reasons.
They do not have ffmpeg installed of their shared servers.
Connection limit is 25; and videos generally have a buffer zone;
I know that arvixe has ffmpeg installed on their shared servers, but they aren't as reliable as hg is.