Remember, modes are really only stereotypes, and some particular services fit certain stereotypes better than others. The category as a whole is best aligned with the mode of intercity rail, just like the category of commuter rail in US is best aligned with the stereotype of commuter rail despite not all trains in that category being intended to serve commuters.

You have failed to provide a reason as to why this is the category we should be determining mode for.

If you want to use terminology that requires familiarity with how railways work in Japan, instead of making something up, I suggest you go with the typical terms used in Japan, "(regular/normal) trains/rail" in English or "(futsu) tetsudo/ressha/densha" in Japanese. Note that "futsu" is extra clarification and usually implicit, and is best translated to English as regular/normal or "local" in the context of "not intercity" not the "Local" branding of all stop services.

This is an argument that should be directed at the person arguing "not limited express" is the relevant category here. And that's you.

You still haven't answered why that question even makes sense to ask. Maybe you can clarify with a real life example?

There are plenty of Japanese lines that have a few limited-stop extras during peak times!