A finite verb is a verb that specifies the tense or form of the verb whereas a non-finite verb is a verb that does not specify the tense of the verb. In other words, finite verbs change their form according to the number of persons or subjects whereas non-finite verbs do not.
In the given sentence, the subject is "I", and the verb "play". The verb shows the tense "play" and also contains a subject, with a single verb. This is a case of a finite verb.
