Is I run in the subway grammatical? Does it mean the action of running, done inside of a subway?
Interesting difference in American and British English here.
Here in the U.S., if I heard someone say, "I run the subway," I would assume they worked as a manager for the commuter rail service.
Moreover, if they corrected me, and said, "No, I mean, I run inside the subway," then I would imagine that they ran in the railway tunnels, and marvel that they hadn't been arrested or electrocuted yet.
Yet my online dictionary cleared up the matter rather nicely:
So, back to the O.P.'s question: I imagine it would make perfect sense in the U.K., but would be rather confusing to many Americans.
While the sentence "I run in the subway" is entirely grammatical, whether it expresses what you want to express is perhaps debatable.
"I run in the subway" means that you make a habit of it: every day (for example) you go out for a run, and you run in the subway.
If you are describing what you are currently doing, I think it's more likely to be expressed with the present continuous, "I am running in the subway."
Given the comments, if you are actually including the question mark [now edited out] in the quote, "I run in the subway?" is not a grammatical question. "Do I run in the subway?" would be grammatical, meaning "Am I in the habit of running in the subway?" or "Am I running in the subway?" meaning "Am I doing that at the moment?"
As to grammaticality and literal meaning:
But this is all somewhat academic, in more ways than one. Most standard English speakers (even including the varieties that I am mildly aware of) just don't talk like that, they just don't use the simple present form very often. Sure, the construction is what you're taught on the first day of English class (as EFL) and all standard English speakers recognize it as acceptable: 'I run', 'you cry', 'he/she/it talks'. But more often you use the progressing "I am running", or you use a lot of extra qualification "I run in the subway everyday of the week as a workout" or "I always think someone is following me down there, so I run in the subway". But these aren't particularly common situations, at least not semantically.
Also, there's another 'weirdness'. You just don't say 'in the subway'. Sure it's 'grammatical' but, really, what do you mean? The subway car, or the platform or the tunnel (surely no one goes in the tunnel , but that's really the only good stretch to run in, the rest it's just not practical. And you are 'in' what? You ride on the subway car, you are on the subway_ platform, you're not allowed to be in the subway tunnel, and if you refer to the subterranean transportation system for travel, you say 'I took a ride on the subway/Metro/Underground/T/L/etc'. There is no in of the plain and simple 'subway'. Unless you are in a building of the fast-food chain.
The point of all this? Sometimes writers of foreign language learning examples come up with some pretty weird situations.