According to the News on the Web corpus,
closeout is used more than ten times as frequently in the US as the UK, confirming my own feeling that it isn't commonly used in the British-influenced part of the Chi world. So it will be treated as rare in future.
Interestingly, many of the examples of the word in places like Britain and Australia seem to have sports meanings that are not given by dictionaries. Sometimes it seems to describe a game that concludes or decides a series:
It was Mitchell's second 22-point quarter this postseason, with the other coming in the closeout Game 6 against the Thunder.
On other occasions it seems to relate to some type of action in a basketball game:
And while Williamson, and his soaring closeout block on Virginia's De'Andre Hunter, stole the show Saturday, James said the entire Duke team was impressive.
Both of these quotes are from the UK edition of the ESPN website. My own basketball knowledge is minimal. I was perhaps the only person in the universe who hadn't heard of Kobe Bryant before his death.