That strikes me as a rather unhelpful definition.
The City of Westminster is a city, and so is the City of London, but I doubt many of us would describe a Central Line train connecting the two as an “InterCity” train.
On the other hand Gatwick Express (NOT a journey between two cities)
was historically an “InterCity” service under BR.
A more useful definition of “InterCity” would be restricted to the services which were classified as such under BR. I don’t believe Portsmouth - London services ever ran under BR’s InterCity brand.