As the game was going on, I thought it was a strange decision, but after thinking about it, it makes a certain logical sense given the relatively low odds of getting a TD on 4th and Goal from the 11 and how much time was left for NDSU to get a winning drive if the game was tied. Consider these scenarios:
1. Griz go for and get the touchdown and extra point (I'd say there was at best a 25% chance of success, probably less). NDSU now has a little less than 3 minutes to get into field goal range (or get a touchdown), plenty of time for their offense especially with 2 time outs. Montana needs a defensive stop (not necessarily a three and out, but can't give up too much yardage) to force overtime, in which they will have to stop NDSU again at least once more to win. (There is also the chance that the Griz stop NDSU and drive for the game winner themselves, much like what actually happened)
2. Griz go for and fail on 4th and Goal from the 11, probably an incomplete pass. NDSU now has the ball at the 11. Montana needs a quick defensive stop, probably a three and out, to have a chance of putting together a game-tying TD drive to force overtime. Then another defensive stop is needed for the win.
3. Griz make field goal, need a quick defensive stop, probably a three and out, to have a chance to put together a game-winning TD drive.
4. In an offshoot of scenario 1, Griz get the touchdown and attempt and make a two point conversion. Montana still needs a defensive stop to preserve the victory. If the conversion fails, a quick stop and scoring drive is still needed.
No matter what, the defense had to stop NDSU at least once and likely couldn't afford to give up more than one first down. Kicking the field goal put the Griz in position to win the game after they made the stop.