Learn German: Das Kind kriegt ein Geschenk.

Both kriegen and bekommen mean "to get" or "to receive". Kriegen is very common in everyday spoken German and informal situations, while bekommen is a bit more standard and often preferred in writing.

This lesson is about verbs with two objects (dative and accusative). Does kriegen take two objects?

Usually, no. Unlike geben (to give), which takes a receiver (dative) and a thing being given (accusative), kriegen puts the receiver in the subject position (Das Kind). You only need the thing being received as the direct object in the accusative case (ein Geschenk).

Why is it ein Geschenk and not einen Geschenk since it is the direct object?

Geschenk is a neuter noun (das Geschenk). In the accusative case (the direct object), neuter words like ein stay exactly the same as they are in the nominative. Only masculine nouns change to einen.

Does kriegen have anything to do with the German word for war (der Krieg)?

Yes, historically! It originally meant to get something through warfare or a struggle. Today, however, that aggressive meaning is completely gone. It is just a normal, everyday word for getting something, like a present or an email.