'argalis' ultimately comes from Mongolian, specifically the word 'argali', which referred to the wild mountain sheep.

'argali' entered European natural-history usage (via Russian and other Central Asian contacts) in the 18th–19th centuries and was adopted into English as 'argali', with the regular English plural 'argalis' also used.

Initially it named the specific wild sheep species; that basic zoological meaning has been retained in modern usage.