Packages of ham or smoked fish sometimes have a hint like the one I quoted in the title. They are usually stored in the fridge, so one part of the reason to take it out of the fridge and open it earlier is probably just the temperature. But is there some chemical reaction with oxygen that is important for the flavor? I think the packages are sometimes sealed in a pure nitrogen atmosphere.
Some food is indeed packaged in a protective atmosphere. This is done in order to prevent the outer layers of the food from changing due to oxidation.
I am not aware of any food that would be vacuum-sealed or packaged in a protective atmosphere which would benefit from the chemical processes after the package is opened.
The reason why manufacturers suggest opening the package is most likely just to facilitate heat exchange with the surrounding air in order to bring the temperature up to improve the flavor and aroma of the food.
I believe this is to allow the gases used to preserve the food to disapate.
Our meats and seafood are vacuum sealed, greatly reducing the chance of bacteria growth. Due to this process, the concentration of carbon dioxide and nitrogen left in the packaging can cause a sulfur smell when opened. This is normal and can be easily remedied by opening up the package and allowing it to sit for a couple of minutes.