This is already working without explicitly adding support for it. The trick to it was that the drop down menu required focus before you could use arrow keys to navigate it, and while clicking on a button was changing its value, it was not giving it focus. I fixed this by giving focus to the SELECT element whenever a button above it is clicked. Once you give it focus, whether by clicking on it or on one of the buttons above it, you can navigate through it with the keyboard. The left arrow, up arrow, and PgUp button all move the selected line up, which takes it back to previous moves. The right arrow, down arrow, and PgDn button all move the selected line down, which moves it ahead to later moves. Also, the Home button takes it to the first move, and the End button takes it to the last move.
This is already working without explicitly adding support for it. The trick to it was that the drop down menu required focus before you could use arrow keys to navigate it, and while clicking on a button was changing its value, it was not giving it focus. I fixed this by giving focus to the SELECT element whenever a button above it is clicked. Once you give it focus, whether by clicking on it or on one of the buttons above it, you can navigate through it with the keyboard. The left arrow, up arrow, and PgUp button all move the selected line up, which takes it back to previous moves. The right arrow, down arrow, and PgDn button all move the selected line down, which moves it ahead to later moves. Also, the Home button takes it to the first move, and the End button takes it to the last move.