I think it's more that English is a bit weird here. Why just 'work'? The person who says this is obviously going to their own work so they should by normal English logic (is that an oxymoron or what?) say I am going to my work. Which would then be jobbet in Swedish because we feel the definite is enough when it's obvious we're talking about our own one. Actually come to think of it, you do say it that way as long as you stick with job – at least I don't think I've heard 'I take the subway to job'. – So maybe we should have translated the sentence that way to begin with. On the other hand, unfortunately it's very common to say till jobbet in Swedish and to work in English. And those two are the most natural ways of saying it in our respective languages. So you could say …till arbetet or …till mitt arbete in Swedish, but that's much less common. And 'I take the subway to my job' isn't the most natural/common way of saying it in English, '…to work' is.
No, we say tar tunnelbanan. Isn't that the same in English btw? 'I take the subway', not just 'I take subway'.
So why is it "tunnelbana" instead of "tunnelbanan" in this case with the verb åker?
Interesting question. It may be that in tar tunnelbanan/'take the subway' we're thinking of something more specific whereas in åker tunnelbana/'go by subway' the subway is more like an adverb, answering the question "how?".
At the end of the day, it's just that languages make "choices" so that some ways of expressing things become the norm and others don't, but the reason for this choice could be something along these lines.