Present participle: I watched the baby (who was) playing on her mother's lap.
The array 'who was playing on her mother's lap' functions as a relative clause. It modifies the noun 'baby'. Take out the 'who was' part and the result is called a reduced relative clause. It functions as an adjectival phrase with the present participle 'playing' as the head of that phrase.
Note, is + ing verbs forms are made up of two verbal units: A form of the verb BE (is, are, am, was, were, etc.) and a present participle.
All the best.