BrE speakers use both. I think I use 'match' more often than 'game' - and I think most other BrE speakers do the same. Might make a difference with the sport... I'd certainly say 'football/rugby/cricket/basketball match'...thinking about it I'd use 'match' for competitive games between two teams or two players, so for example "I want to watch the match between Murray and Federer", but I'd use game for less competitive things "My wife and I had a game of badminton at the Sports Centre yesterday." (even though my wife can be pretty competitive!!)

Chris Tooze is right to say that BrE speakers say both, and his other comments are helpful. For this particular sentence, I would tend to say "game" because of the alliteration (https://www.oxfordlearnersdictionaries.com/definition/english/alliteration?q=alliteration). In informal spoken English, it would be "The players scored twenty goals a game."