Is Kitchen cooktop venting required?
Because code varies by region, it's difficult to say yes or no to this.

Typically you only really need ventilation to the outside if you have a gas range.  Often the hoods on top of electric cook tops just recirculate the air inside and don't actually vent outside.  That being said, the often have a carbon filter which is handy for removing odors.  They also usually have a light on them which is also handy for cooking.