Is the word play an adverb?

No, the Word 'play' is a noun (play, plays) and a verb (play, plays, playing, played).
An adverb is a Word that modifies a verb, an adjective, or another adverb.

Examples:
I have tickets to the new play. (noun)
I sent the children to play while I make lunch. (verb)
The children are playing quietly with Legos. (the adverb 'quietly' modifies the verb 'playing')