My question, though, is whether this is used the same was as Americans use the term. Do Russians mean to refer to soccer ("true" football") exclusively, or do they refer to either sport with the same word, like Americans?
I assume it's similar to the way it's referred to in Hebrew. In Hebrew, soccer/British football is called כדור רגל/kadur regel (literally "ball [of] foot") and American football is referred to as כדורגל אמריקאי/kaduregel amerikai
In the context of the full sentence, the audio for смотрю sounds correct. But if you play the audio for the individual word, it sounds a little more clipped -- I think it's still saying смотрю but I can see why someone could hear смотрим instead; it does sound very close.
Why is this 'are you watching' and not 'do you watch'? I've now seen this exact same verb construction so many times, each translated in a different way, some with the -ing meaning and some not. They have such different meanings - how do you know which is implied?