आमिर खेलना जाता है is grammatically incorrect. This is because जाना is an intransitive verb and cannot take a direct object. The oblique form खेलने must thus be used.

You can use the normal infinitive with transitive verbs. For example, "Amir knows how to play" is आमिर खेलना जानता है । because जानना is a transitive verb.