That’s exactly why they pulled the goalie.
It’s a pretty common thing in hockey. It all depends on the coach and the score of the game. If a team is down by 2+, they usually pull the goalie earlier than if they are only down by 1.
Some coaches are more daring about it. Like Housley, for example, during the Sabres 1st game of the year pulled the goalie with 5 minutes left in the game. They were down 3-0 though.
That used to be somewhat unusual (and it still is to some degree) to pull a goalie with that much time left. But Patrick Roy kind of started that trend his first season coaching the Avalanche, and it worked for Colorado. Then you started to see other coaches pulling their goalie earlier than normal.
Roy actually pulled his goalie a few different times with 10+ minutes remaining in the game (once with 13mins left)! I don’t know of any other coaches who have repeated that off hand.
Here’s a good article on it from a few years ago, if you are interested -
https://fivethirtyeight.com/features/nhl-coaches-are-pulling-goalies-earlier-than-ever/