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.