While I think you could fix it with some clamps, wood glue and filler, I don't know if it would be worth it. It might not stay fixed for long.
Humidors tend to be something where you get what you pay for. I still have my first one, which I've had close to twenty years now. It wasn't a cheap one, but it's solid wood, still looks like new and holds humidity perfectly. Lot of cigars have cycled through that little desktop. My cabinet, which I got a few years back, cost an obscene amount but will probably outlast me by a good hundred years. Maybe a couple of hundred.
If you really want a humidor, pay the money and get one of quality. If you just want storage, go with a cooler - it's the best bang for your buck.