I read it as implied that you can only go up between hands, since it does not even contemplate taking away chips.
The author assumes players want more, not less, in play.
I checked the versions of Hoyle from 1880 and 1953, and they are edited differently but make the same point.
From the passage you shared
"no player is allowed either to increase or diminish that amount while he has any cards in front of him"