Its actually not......... Laminate to bare wood, not on top of paper laminate! You've just stuck your expensive laminate to paper... NOT a good option.
If you want to do it on the cheap I'd say prime and paint. Mess or not though, theres really no substitute for a good old fashioned stripping. Sorry.

With just paint you'll still see the woodgrain through the paint. I've had this happen with a cheap shelf I've painted before. Its not neccesarily a bad look, but be warned it will peek through.