I don't agree. Depending on context, it can be both. The context here is not given. Peronally, I would actually prefer "Do you eat everything" over the other meaning. For "are you eating all of it" I would rather use "Ĉu vi povas manĝi ĉion?" (Are you sure? Are you able to do that?). If I want to emphasize the continuous form in an unclear context, I put "nun" somewhere in the sentence.
It's not everything in front of him; if you gave me a steak, mashed potatoes, and a bowl of putting, I might look at the pudding and eat "all of it" without eating everything. Likewise, I might eat "everything" in front of me without eating everything in the world.
You also might be at a buffet and have an election of various foods, and take some of everything instead of only the meat.