"tôi ăn con gà kia." Another correct answer would be "Mình ăn con gà kia". For English speakers, this is easier. Since you can associate "mình" with me/mir/moi. It also sound much friendlier! I don't think anybody in Vietnam use "Tôi" much these days XD! There are few exceptions tho. "Mình" can also means "We", but for now, you don't have to worry about it :).
"Toi" and "Tao" are actually used to show aggression or who is the dominant one. Foreigners use it cause they don't know this
I was wondering why "thịt gà" is not used here. Wouldn't be better to say "Mình ăn thịt gà này" ?
If you used thịt gà that would mean that you are referring to this chicken meat. If you say con gà you are referring to a live chicken.