I think the individual parts of it are:
- 遊{あそ}ばにゃ → 遊{あそ}ばなきゃ → 遊{あそ}ばなければ (see also 遊ぶ)
unless one plays/unless one has fun/unless one enjoys oneself
loss/disadvantage
(mainly for emphasis, I don't think it changes the meaning much here)
- だろう (the plain form of the polite でしょう)
I think
though
(an exclamation, sometimes translated as "oh!" or "hey!" etc)
...遊ばにゃ損ってなもんだろうがおう!
...遊ばなければ損というようなものでしょうがおう!
...It's a loss if you don't enjoy yourself I think though. Alright!
I think that translation loses a lot of the feel of the original colloquial text though.
EDIT: For the time being, I've assumed the "な" was a typo. Also hopefully fixed the exclamation part.