I would call it a hybrid. It has a suspension fork and near-mountain bike gearing. You can do a lot of riding on that bike, and I think it's a lovely gift! A perfect first bike for someone who hasn't ridden as an adult.

The step-through frame is just style and accessibility and has nothing to do with whether it's a "cruiser" or a hybrid. Cruisers are usually single speeds -- this bike has a triple up front and low gearing in the back. These are all just marketing terms, anyway ... the line between "comfort" and "hybrid" is pretty blurred, particularly since some relaxed geometry road bikes are called comfort bikes depending on the manufacturer.