I personally wouldn't want to pay any extra for an NES with that sticker, even if the sticker is rare. It certainly doesn't look aesthetically pleasing as it is. I'd say just put it on eBay and hope for the best?
If you could actually figure out who owned it previously and have a record of their participation in the Nintendo World Championship you could probably boost the value since you'd be attaching an actual story to the console.
But I don't know! I've never been a hardcore Nintendo collector-type! Maybe someone would desperately want it?
The one of the two stickers that matters is fairly fubar, legible but fubar. I don't think anyone could give you a price that you could hold them to. If it were only lightly damaged or not at all someone probably would pay pretty nicely for it. At this point I could only imagine how little it may get over the value of a NES unfortunately.
If you wish to get paid on it as you have another NES lying around I'd just throw it on ebay with a minimum value you'd feel it worth starting at, or just put a decently high number with a best offer from the beginning and see what shakes out.
And I had a sub with NP mag up until the first issue Future took over and their not so happy staff started taking digs at Nintendo for some childish reason and canceled it. I never got a sticker like that with my sub so odds are, especially due to that damage, it's real. It would be fairly dumb to make a fake and wear it like that.
I know that with the semi-finalist one, you actually had to compete and get the semi-finalist sticker in order to be let back in at the next round the following day. That's why mine has a Sharpie slash through it. It was a free pass to return and they marked it when I went through the gate. I would just assume that the finalist stickers would be the same.