Eldritch Horror test resolutions in other board games
Hello and welcome to the world of modern board games. The mechanism you are talking about is a common mechanism for a number of board games. 

You are correct that Arkham Horror uses this exact mechanism. 

Other games use a similar mechanism: 


Summoner Wars - uses a 6 sided die for combat but here you typically hit on a 3+
Eclipse - uses a 6 sided die for combat but here you initially only hit on a 6


I'm quite positive there are dozens more that could be listed, but those were the first games that came to mind that I was familiar with.