Seamless and GrubHub operate like that, they just bring an online interface (and easy management) to the store's pre-existing delivery employees.
AFAIK, Postmates and Caviar are the only two companies going with the two-party model, but employing their own delivery drivers/couriers.
Do you live in New York? The "free" delivery with tips model is how things work in New York, but i've never seen it elsewhere.
In SF takeout places only rarely offer delivery.