Maybe, I also find it strange, the literal translation... But I remember when I was learning English I always found it very strange that something that is not a person could work. Because in Spanish only persons work; not machines, not cars, not pens, only persons. Machines, cars and pens 'function'. Funny, ha!
I find this fairly straightforward. It's a little weird that we say "the heating works" in English; I actually think "goes" makes more sense.
This sentences isn't weird if we say: "Today the heater does not work". I did that and it's correct. Duolingo should include the meaning "heater" here.
Isn't 'the heating' just the collective system of heaters in a given building? I think 'the heater', indicating the individual machine/object is 'il riscaldatore', or more colloquially put: 'la stufa'.
I think the translation "heat" it what flies here. As in the fairly idiomatic phrase "oh crap, the heat is out today."
I think the weird part, when translating to English, is the use of the verb "andare" to express functionality.