The particle で is not only used to mark locations but has another use (among others) - marking means of doing something (tools). Like “with” and “by” in English.
Examples:
getting to work by bus, cutting cake with a knife, speaking in English etc
So you could say it means something along:
“Shall we communicate by means of Japanese?”
By the way, を also does not only mark direct object (answers to question "who/what is being verbed - I am studying(verbing) Japanese), but also has another uses I superficially explained here:
By looking at the grammar point you linked to, I saw that this use of で is explained later in Genki - I’m just not that far into the book There is even the same example mentioned.