Has an NHL game ever ended 9-7?
It has. 9-7 has been a NHL final 20 times in 70,352 games. The first was Chicago Black Hawks beat New York Rangers on February 26, 1947; the latest was Detroit Red Wings beat Tampa Bay Lightning on December 5, 1992.
That makes 9-7 the 60th most common final score out of 95 that have ever occurred in NHL. One point away, 10-7 has happened 11 times and 9-8 has happened 5 times. Nearly all of its occurrences fall between 1980 and 2009.