Not addressing the -off part directly, but face-off in hockey comes from its relative, lacrosse. The OED's first citation is from 1889:
1889 Appletons' Ann. Cycl. for 1885 520/2 A goal may be scored within a minute's play from the face-off, or it may require half an hour's struggle.
I found several antedatings in 1886, the earliest from August 1886.
First, Harper's Young People (24 August 1886, vol. 7, no. 856, p.684):
When the ball is started, all the players, with the ex-
ception of the goal-keepers, should be paired off all over
the ﬁeld, each man close to one of his opponents. If the
possession of the ball is disputed by the two players who
“face off,” let the others approach near them, but not near
enough to interfere with their movements. They will
each seek to “ tip" the ball with his stick or foot to
some friend who has thus approached, and he will have a
much better chance of securing it than if he had blindly
rushed in and entangled himself in a “scrimmage.” Of
course a brilliant dash in between the two players will
sometimes secure the ball, but wait until you see the
chance. Don’t fight for the ball blindly as if with your
eyes shut. Use both eye to see and brain to calculate,
and just at the right moment act with all the courage and
strength that you have.
Interestingly, the second talks of a proposed rule change to replace the face-off.
Outing : Sport, Adventure, Travel, Fiction (August 1886, vol .8, no. 5, p.581):
A new rule has been proposed in the United
States Convention, which was received with
some favor, and is worthy of consideration. At
present, the opening play of a game, from the
"face off" often results in an undesirable scrim-
mage. This is true even when the game is
being played by the best Canadian teams. It is
a bad impression to give, as a first one, to an
audience. By abolishing it, the " face off" and
all its finesse (for it has something of skill in it),
can be retained to be used in case of fowls, etc.,
during the game.