Is it possible to repair a SNES cartridge with broken/worn contacts/pins?

You have 1 pin that's completely worn off, and another that's getting there quick. A third pin looks like the connection is completely broken, and a few more look like they might need some work.

This won't work.

I would only keep the game if it's worth >$100. Otherwise the time and cost will likely not be worth it. The repairs aren't really that difficult for someone who's done it before, but finding someone experienced might be an issue.

I'm not sure if you can apply it here, but I know there is a way to fix damaged paths on circuit board. Here is the link that demonstrates how to do it:

In short, it describes how to remove the damaged section of a circuit trace, which tools to use and how to replace it with a new trace.

In your case, I would first try to identify which paths are damaged. You can use continuity test of a multimeter for that. Almost any digital multimeter has that option nowaday. And then, you can apply the method described above on each such path.

You might need neurosurgical skills to do it on such a small board, but it should be possible.