I think the .rec format is something like this: player moves left, player see's object such and such, player does this, player does that (A bit more complicated but you get the idea). When you play an .rec you actually create your own server and spawn and make everything do what it was doing when you recorded the .rec. I'm not 100% sure what it does but I think its something along those lines.
Unless you have all the files that badspots server has you're probably not going to be able to play .rec's anytime soon.