Gerund functions as a noun, whereas present participle functions either as part of verb or as an adjective. So:
In "Reading should be done in the room", Reading is a gerund used as
In "I like reading", reading is a gerund used as object;
In "I look forward to reading your book", reading is a gerund used as object to the preposition "to"; but
In "I am reading your book", reading is a present participle used as part of predicate;
In "He stays in the room, reading his book", reading is a present participle;
In short, gerund acts more like a noun, whereas present participle acts more like a verb or adjective. So:
In "a sleeping man", sleeping is a present participle, as the action of sleeping is from the man, that is, the man is sleeping; but
In "Sleeping car", sleeping is a gerund, as the action of sleeping is not from the car, that is, the car is not sleeping, but the people in the car sleeping.
So in your sentence, "playing" is a present participle.
Hope this helps.
- For Teachers