How long will a shooter's sandwich keep?

The shooter's sandwich you linked involves cooked mushrooms and fried steaks. In contemporary food safety practice, this is not shelf-stable at all. It can be held 3-5 days in the fridge, or up to 2 hours at room temperature.

I can imagine that hunters did take it on longer trips historically. They lived in a time when mild food poisoning (symptoms limited to bloating and light diarrhoe) was commonplace, and the average person experienced it as often as the common cold, if not a bit more frequently. More serious types of foodborne illness were less frequent, but still appeared with some regularity in a given population.

There are two reasons we don't eat this way today. First, our standard of living is higher. We have the possibility to drastically reduce our risk of food-borne illness by choosing nutritious shelf-stable food for situations we need it, and we have much higher expectations of our own quality of life, including the expectation that the chance of getting bloating from a sandwich should be close to zero, not close to 10%. Second, our meat today well may have much more pathogen contamination than in the past. If you slaughter one healthy animal in your small farm, the worst you get spread over the meat are some E. coli from inside its own guts, and normal E. coli don't cause too bad symptoms (mutations can be very dangerous, but they are also exceedingly rare). Today, animals are penned together by the thousands, exchanging exotic pathogens while still alive, and then are slaughtered and eviscerated in efficient conveyor-like manner, so that if one cow had some unpleasant bacteria from somewhere, they will probably cross-contaminate the steaks from hundreds of other cows slaughtered in the same shift.

Bottom line: It is absolutely not safe. You are free to decide to take the risk and eat it, but by the usual standards in the food industry, this is an unacceptably high risk, and it is foolish to take it.

First let me point out that most of these ingredients that people would consider "dangerous" if left out, have all been cooked in this recipe. The most likely place that any bacterium would be introduced is using unwashed hands to pluck the bread from the loaf. I have made this myself, let the sandwich flatten overnight, refrigerated for 24 hours, then taken out on a hiking trip, where it provided me lunch for the following week stored in a zip=lock bag in my back-pack.