The orchid listed on the linked site as being the basis for the drink is Orchis macula. According to a web search this orchid, while having a wide distribution, is described as "rare" or "endangered" in some locales and is a protected species in the Netherlands.

Traffic in certain herbs has severely depleted them in the wild (goldenseal and ginseng are just two examples). I would hate to see Orchis macula collected to the point of extinction due to Internet promotion of its reputed (but apparently, not documented) value to "the intestines".

Salep (or salop) was traditionally made with quite a bit of Ginger ... and that is well-known to be good for upset tummies.

I think the orchid got the credit for the work the Ginger did.

BTW, the original intent of salep, like most orchid-based drinks was an aphrodisiac, not a digestive aid. Diasatyrion or plain Satyrion (look up "satyr") was the original name of the plant.