Do we need to include .nyc_output or should we just put that directory in .gitignore
Yes, it should be included in the .gitignore; because, it is an intermediate cache of data that is used for when you eventually run nyc report.
As an intermediate store, you don't wan to track the contents; because, they are not actually the "source". Source control systems do much better when they only track true sources, and don't attempt to revision intermediate files.