No need to be super wary. Don't you know that some Chinese employers of foreign teachers find it vey difficult to fill such vacancies, especially those at schools in small satellite cities/towns?
Actually, it's a good thing for foreigners seeking teaching jobs in China that the situation is like that.
It's a refreshing change to be offered a teaching post without so much as a telephone interview first, so unlike what happens in the West. I've often accepted such jobs, and without dire consequences. The more one is in demand, the better one is treated, that's been my experience here as a rule. Do yourself a favor by ceasing to judge the way things are done here against western norms - they simply don't apply!