I think this covers it:
18-5 By Another Ball
If a
ball in play and at rest is
moved by another ball in motion after a
stroke, the
moved ball must be replaced.
Relevant Definitions:
Ball in Play
A ball is
“in play’’ as soon as the player has made a
stroke on the
teeing ground. It remains
in play until it is
holed, except when it is
lost, out of bounds or lifted, or another ball has been
substituted whether or not the substitution is permitted; a ball so
substituted becomes the
ball in play.
Move or Moved
A ball is deemed to have
“moved’’ if it leaves its position and comes to rest in any other place.
Stroke
A
“stroke’’ is the forward movement of the club made with the intention of striking at and moving the ball, but if a player checks his downswing voluntarily before the clubhead reaches the ball he has not made a
stroke.
Note also that his rule states that you must not mark your ball anywhere EXCEPT the green unless specifically requested to do so by your competitor:
22-2 Ball Interfering with Play
Except when a ball is in motion, if a player considers that the ball of another player might interfere with his play, he may have it lifted.
A ball lifted under this Rule must be replaced (see Rule 20-3). The ball must not be cleaned unless it lies on the putting green (see Rule 21).
In stroke play, a player required to lift his ball may play first rather than lift the ball.
Note: Except on the putting green, a player may not lift his ball solely because he considers that it might interfere with the play of another player. If a player lifts his ball without being asked to do so, he incurs a penalty of one stroke for a breach of Rule 18-2a, but there is no additional penalty under Rule 22.
Penalty for Breach of Rule:
Match play — Loss of hole; Stroke play — Two strokes.
So, your ball was in play, you were not required to lift your ball unless your opponent asked you to do so, but could have done so, since you were on the green.
Once your ball was struck by the other ball, you were required to replace the ball and putt out. You didn't putt out. In stroke play you would be disqualified under:
3-2 Failure to Hole Out
If a competitor fails to hole out at any hole and does not correct his mistake before he makes a stroke on the next teeing ground or, in the case of the last hole of the round, before he leaves the putting green, he is disqualified.