I can only assume that the concept of when a ball was out of play was thought to be so obvious that no explanation was considered necessary!
The preamble to the 1846 Laws includes[LAWS]The following book of Rules is to be regarded rather as a set of Decisions on certain disputed points in Football, than as containing all the Laws of the Game, which are too well known to render any explanation necessary to Rugbeians.[/LAWS](The title page refers to both Laws and Rules.)
The 1862 law book has this in the preamble[LAWS]When the ball goes outside the line of touch, the first player who touches it down, takes it and walks with it to the touch line, and throws it out at right angles to the line of touch, or bounds it outside the line of touch, (i.e. in the field) and catches it again, and runs with it, or drop-kicks it himself.[/LAWS]
and this in the laws[LAWS]32. TOUCH. A ball in touch is dead; consequently the first player on his side must in any case touch it down, bring it to the edge of touch, and throw it straight out, but may take it himself if he can.
[/LAWS] That supports the claim that it is called "touch" because a player had to touch it down.
Note also the phrase "on his side". A player "off his side" could not touch the ball down because he was out of play.