It isn't super popular, no. I think the requirements are pretty strict if I remember correctly (edit: https://www.iana.org/domains/int/policy).
I think esa.int is probably one of the more popular .int domains on HN: https://news.ycombinator.com/from?site=esa.int
In meteorology, you also have ecmwf.int (the European Center for Medium-Range Weather Forecasts).
interpol.int also comes to mind.
It would have been better if the requirements also included the domain name had to start with a letter between I and N (inclusive).
But I guess this is what you get when these things get away from technologists.
Other notable .int domains:
• World Health Organization - https://who.int
• NATO - https://nato.int
• Council of Europe - https://coe.int
• Mercosur - https://mercosur.int
• African Union - https://au.int
• EFTA - https://efta.int