At the risk of spoiling the joke, here is the <
Snopes info about that site>.
As far as I know, a "cookie" will only include information about you that you enter in a page. This site would already have the info it would write to a cookie, it would not, then, be available to any other site via that cookie. Nor would they have 'harvested' your info from that cookie since they had to have it, via your typing it in, in order to even write/create the cookie.
Cookies are more likely to contain information about your use of a site and even passwords you might have used to keep you logged in. Certainly info about you can be in a cookie, but it is usually only the site that creates the cookie that can even find it on your drive. So, if you don't want your own info in a cookie or a sites database, don't provide it.
You shouldn't be typing in personal info in a site you don't trust, anyway.
In this case, it's a prank that's been around for several years. And you don't even have to enter your own info, you'll get the same results, no matter what you enter.