There will almost always be problems and issues when a new MMO or significant game is released. Many players are complaining about various problems in New World. Steam must be running in order to play this game,” is a recent issue that many gamers are encountering. To fix this, make sure you’re logged into Steam first, and then try the game again.
It’s possible that this problem is related to New World’s “Untrusted system file” error. Many players are baffled as to why and how this occurs in New World. EAC Error requires Steam to be open in order to play. Check out the suggestions listed below and see if they work for you.

How to fix New World unable to launch due to EAC Connection Error
It appears that the most likely cause of this mistake is the most recent Steam update, as users have been reporting a number of new issues following this update. Having either of these problems prevents people from joining the game, which is incredibly inconvenient.
Check out some of the possible solutions to the New World Steam must be running New World EAC Error: Steam Must Be Running (Untrusted System File) in order to play this game and EAC Error problems.