I have come full circle. I loved processed American cheese food (pacf) when I was a kid because I was a kid. Then I got into fancy sliced cheeses like cheddar and Gouda. But they don't melt as nicely! So now back to pacf for burgers and melts because it is the best ingredient for that job.
I've never heard of Chester cheese. There's Cheshire cheese, but that's quite crumbly and wouldn't hold up to being packaged like this. You might also be thinking of cheddar. A genuine cheddar would be too brittle, but in modern marketing, cheddar is often shorthand for any homogenous, yellow cheese. So this stuff might be described as cheddar on the packet.
I think this stuff is more of a cheese-flavoured sauce, that they inject into the bags and leave to set. It's more an invention of the convenience food industry, than any culinary tradition.
That's an egregious example because you can find better sliced cheese (store brand) for much cheaper than Sargento even, but still disturbing to see how expensive those singles really are.