Roel van der Goot writes in " Awari Retrograde Analysis":

"Board games can more or less divided be divided into two categories. The first
category consists of games where the pieces on the board increases, because a
player's move consists of putting a piece on the board. (...) The second
category consists of games where the number of pieces on the board decreases
because the player can do a move that captures pieces. (...)"

http://www.springerlink.com/content/bmx0gpmy1rvxmf17/

Is this correct?

No, it's not.

(1)
There are games in which the number of counters remains stable throughout the
game: Type II, 4-rank mancala games (Bao, Omweso, //HUS), but also Neutreeko,
Quartetto and Shogi.

(2)
There are games in which the number of counters increases and decreases:
Nine-Men's Morris & Dvonn (in the placement phase: increase; then: decrease - in
Dvonn de facto too as there is no "unstacking" mechanism).

------
Ralf