Window Crank stem
Yep, looks like the whole worm gear setup here is stripped. This isn't something you can repair, unfortunately, since these are machine-pressed at the factory. Your only option is to replace the entire operator mechanism.
We can help, but I need to see a picture of the complete operator mechanism out of the window before I can make a suggestion. It's important to see it out to ensure that no important details are obscured by the window frame.
Once I see it out, I can check out inventory for a match. I'm confident that we have one, though probably a more modern version. They don't make this exact style base anymore but the new ones work in all the same old applications just fine.