Force Out Play

[SC Ump]

It's in those rulebooks, but just perhaps not in the wording you expected. All the rulebooks state similarly:

For a legal "tag" (not what you asked about), the runner must be tagged with the ball or with the hand or glove holding the ball.

In a "force" play (your situation), the fielder need only touch the base while in possession of the ball.

In your play, the fielder had possession of the ball (in the bare hand) and touched the base (with the glove) so this would have been an out if it were done prior to the runner reaching the base.