I think that is a Hybrid w/ 700c wheels. Back in the early days of the Hybrid several companies had 'cross' in the model name of one of their hybrids. Specialized had a crossroads I think schwinn used crosstown.
I never saw shifters like this but it is a good idea!
For $80 I would go look if it has decent components it would make a great commuter.
OH I just saw the pedal comment. Take a pedal with you (left one) if it does screw in

you need a new arm so that is a good negociating point.
This might be a '91ish maybe 200gs level, check for a ChroMo fork, if doesn't have one pass a keeper.