1. What does it mean?
드가자 is a playful compressed pronunciation of 들어가자, let's go in. In streams, games, and casual talk it can urge people to enter, join in, or launch into an activity.
Also written or said as 드가자고, deugaja
2. The nuance
It is intentionally informal rather than standard written Korean. The activity comes from context; the phrase by itself says nothing about whether a challenge or financial bet is sensible.
3. Examples
“대기실 준비 끝났으면 드가자.”
If everyone's ready in the lobby, let's get in there.
“비도 그쳤으니 산책 드가자고 했어.”
Once the rain stopped, I said, 'Let's get into that walk.'
Sources
References support the meaning and usage. Example sentences are written for NoCapWiki.