"Du isst am Tisch."
No it is not. "Am Tisch" means "An dem Tisch" means "At the table". Can't mean anything else. "On the table" would be "AUF dem Tisch".
The differences between English "at" and "on" can be very confusing if you are not a native English speaker. The phrases "eat on the table" and "eat at the table" imply something slightly different in English. If you eat on the table it suggests that you climbed up and sat on the table and then ate. Which people sometimes do at parks at picnic tables, but the more common thing is to sit on a chair or bench while the food is on the table. At that point you are eating at the table.
would "Ihr essen am Tisch" be an alternative answer? or does that make it plural?