I think it's a great policy that works in general for the betterment of all. I do not camp with pet animals but would be more inclined to stay at a campground that allows dogs if I knew the owners were that dedicated to keeping the place clean + comfortable for dog owners and those without; transients and long term guests.
As for how they would collect from guests, short or long term? Charge the credit/ debit card and possibly request a deposit from cash paying guests. Were I running the campground I'd also take a pic of the dog and attach it to the file so subsequent tests weren't needed.
Should cat poo or mini pig poo be a problem I'm sure they can be added to the policy at a different time.
Having worked in hotels, restaurants, and property mgmt for most of my adult life, I can tell you there are A LOT of people w/ piggish habits wandering amongst us AND it doesn't matter if the place is high or low end, transient or long term.