The obvious looking answer would seem to be
except that "having soldiers and different animal species" doesn't fit well:
as chess really only has horses, and they're not even called that.
Also, this is far too obvious an answer, so I sincerely hope it's not Chess.
So I'd offer instead:
I am played in black and white
The players in Shogi are "Black" and "White"
though probably not a game of might
It's a strategy game won by capturing the king, not by killing all the opponents
Half of the field gets loaded at start
with equal forces on either part
This game is played on a $9\times9$ board, and each player begins with 20 pieces -
$20+20=40$ is as close to half of $81$ as you can get.
Both players have equal forces.
It represents a war with pieces
having soldiers and different animal species
There are soldiers ("foot soldiers" and "generals") and different animal species: "horses" and "dragons"
Linked to the above, fill in the following blank:
__, B, N, R, Q, K
Shogi has bishops, knights, rooks, queens, kings with the familiar letters.
It also has "G"old Generals, "S"ilver Generals, "L"ances, and "P"awns,
plus promoted "+" versions of most of these.
So—trick question... the blank would contain, probably: G, S, L, P