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.
It's the same for nouns.
Nouns that are direct objects of a verb don't take the oblique case because there is no postposition in between.
When a noun is an indirect object of a verb, a postposition is present between them and the noun is the object of that postposition. So, the noun should be in the oblique case.
Eg: मैं यह गाना जानता हूँ (I know this song)- 'यह गाना' is a direct object of जानना. So, it's not in the oblique case.
मैं उस आदमी को जानता हूँ (I know that man)- 'वह आदमी' is an indirect object of जानना. So, it's in the oblique case form 'उस आदमी'