で遊んでるよ

play with something, to be playing at [a place]

→ で
phrase Uncommon #19,397
play with something で marks the thing used as a plaything; 遊んでる is a casual form of 遊んでいる.
JA: 妹は人形で遊んでるよ。
EN: My little sister is playing with a doll.

子供たちは、ブロックで遊んでるよ。

The kids are playing with blocks.

子供たちがビー玉で遊んでるよ。

The children are playing with marbles.

子猫の一匹がトイレットペーパーの芯で遊んでるよ。

One of the kittens is playing with a toilet paper roll.

トムはメアリーとジョンと一緒にトランプで遊んでるよ。

Tom is playing cards with Mary and John.

妹は人形で遊んでるよ。

My little sister is playing with dolls.

トムとメアリーは、公園でシャボン玉で遊んでるよ。

Tom and Mary are playing with bubbles in the park.

phrase Rare #42,131
to be playing at [a place] で marks where the activity takes place. This casual expression tells the listener that someone is playing there.
JA: 子供たちは公園で遊んでるよ。
EN: The kids are playing in the park.

トムはあっちで遊んでるよ。

Tom is playing over there.

子供らは外で遊んでるよ。

The kids are playing outside.

子供たちは公園で遊んでるよ。

The kids are playing in the park.

子供たちは家の外で遊んでるよ。

The kids are playing outside the house.