Since the drink is not carbonated, no liquid has been escaping the bottle, and the components don't seem to be able to participate in any kind of chemical reactions involving gaseous products, I assume the gas that's been leaked is air.
I also cannot imagine any kind of chemical reaction involving consumption of this amount of air leading to such a severe bottle deformation. My theory is that air simply escaped over time through the bottleneck. There are 2 parts made of 2 materials with different thermal expansion coefficients:
- the bottle itself (polyethylene #1 (PET), or polyethylene terephthalate (PETE));
- the screw cap (polypropylene (PP)).
Due to the construction of the joint, both parts basically act as a pressure equalization valve. I suspect that the coefficients of thermal expansion are chosen in such a way that when heated, excess gas would slowly escape in order to minimize the risk of explosion when the storing conditions for the finished product is not met. So, when the bottle is heated, the air is slowly leaking out. Once the temperature drops, the "valve" closes and the process stops. Over the course of 10 years, there surely were many temperature fluctuations making air leave the bottle little-by-little.