In Portuguese "futebol" doesn't mean both sports. It means that played with feet only, and a round ball. The other is called "futebol americano".
Yeah, and only americans call futebol soccer (while the rest of the world says football)
That's not true. It's soccer in a lot of countries, including Canada, Australia, New Zealand, parts of Africa, Ireland, etc...
Can someone tell me how we know the first person singular is assumed by this sentence which uses neither eu or a conjugation of jogar?
Probably for not being a confusion between "american football" and "soccer". Indeed, europeans never say "soccer" :)