Likely this would be a slang expression by a younger person which means playing games on their phone.
More correct, or natural to people who speak whole sentences might be
I am playing mobile phone games.
I am playing games on my mobile phone.
I am playing games on my mobile. <-- more common, some places.
I am playing games on my cell.
I am playing games on my cellphone.
I am playing games on my smartphone.
.
same for
I am going to play .....