That would be “at my son." If you meant the personal 'a', it doesn't apply here. 'son' is not the direct object. A direct object is the noun which is being 'verbed'. 'son' is not being 'played'.
A good indication that the personal 'a' is unnecessary is the use of the word with/con. “(verb) con a..." doesn't make sense.
I wrote "Play with my son", [as in telling someone to play with my son]. This was not accepted even though the word 'play' by itself is listed under word meaning.
Susie: affirmative commands are not given in the first person singular. In your English sentence the subject is you not I. Therefore, you need a Spanish "you" form, too: tu or usted.
Refresher: In Spanish, the verb conjugation often gives you such an excellent indication of person and tense that the subject is known without being explicitly stated.
Juego must be first person, singular, indicative present tense. It can't be used in any other way. In English, first person singular is 'I', never 'you'. The 'Yo/I' is left off in Spanish because the verb tells you that it has to be 'I' you are referring to. Translation into English usually necessitates an explicit subject, because our verbs don't give all that information.
in the dropdown from juego, it lists "play with" as one of the options, so why do you need 'con' in the sentence.
drop downs are now always correct. I never trust them. If i don't know a word i will use other resources (dictionaries/web sources, etc.) to find then translation.
It's (poorly) trying to help you understand the use of the word instead of giving you the literal translation. Juego is first person indicative present tense of the verb jugar/play. 'With' is not included in 'juego'.