It's from a video game called Xenogears. You can play rock-paper-scissors with a man and when he loses he says this:
Is it something like "Oh my God!"?
オー・マイ・ガブリーヌ is obviously a pun on オーマイガー ("OMG") and ガブリーヌ, where ガブリーヌ is probably a western surname Gabreanu. But according to this, no one seems to know who ガブリーヌ is: OH MY GABRINO! WHAT DOES THIS XENOGEARS LINE SAY IN JAPANESE?
This character speaks in an idiosyncratic manner in the first place, so probably there is no special meaning.