Did Shakespeare really mean meat pies by baked meats?

Baked for Shakespeare would have meant cooked in an oven, and meat was not restricted to flesh but included any food.

Chickens, however, would probably have been roasted: cooked on a spit over an open flame.

Meats (in the modern sense) were usually baked in a pastry shell of some sort, but again this did not have quite the sense of the modern pie: often the pastry served only as a container and was not eaten.

This line should not be translated literally. The "funeral bak'd meats" is referring to Hamlet's very recently deceased father whose barely cold remains "coldly furnish forth" (laid the table for) the opportunity for his uncle to marry his mother. Remember that Hamlet is disgusted by the marriage taking place so soon, so his language is a bit vitriolic.