Note that "We walk to the cinema" is wrong in this case since "Gå på bio" is a fixed epression in Swedish meaning "Go to the cinema" If you want to say that you walk to the cinema you'd have to change the preposition to "till".
I.e. "Vi går till bion" - "We walk to the cinema"
It would be commonly used elsewhere... certainly it would seem oddly formal or awkward in New Zealand to say "I am going to THE university" if you meant you were going to head to class for a lecture. We would say "going to uni" or "going to varsity". Perhaps the difference is that in the US you might use the word college rather than university? My husband is a university professor here in the US and students here say "I am going to college" to mean either that they are going to attend a certain university or that they are heading to school for a lecture (or whatever). Would you really say "I am going to the college" if you meant you were heading to a class?
(Or even I am going to the school? Doesn't that sound odd to you?)
gå på bio is a set expression meaning 'go to the cinema [and see a movie]'. It's like gå på bio is almost a verb in itself.
If you walk to a specific movie theater, that is går till bion 'walk to the cinema'.
We use the noun without an article like in the first sentence in some cases in Swedish where you prefer to have an article in English. For instance we can say either köpa bil or köpa en bil to mean 'buy a car'. The first version of the sentence expresses the action more in general, with no focus on the specific car. There are some more examples in this thread: https://www.duolingo.com/comment/5824774