The answer lies in the way the LOTG are written.
"A player, substitute or substituted player is sent off if he commits any of the following seven offences:
* denying the opposing team a goal or an obvious goalscoring opportunity by deliberately handling the ball (this does not apply to a goalkeeper within his own penalty area)
* denying an obvious goalscoring opportunity to an opponent moving towards the player’s goal by an offence punishable by a free kick or a penalty kick"
If a player entered the field of play and makes a challenge on an opponent, or stops the ball from entering the goal with any other part of his body other than his arm/hand, then you cannot send the player off for DOGSO, as the wording in the law states that you are sending someone off for an offense punishable by a free kick or penalty. Since a substitute cannot be guilty of committing a foul, you cannot send them off for DOGSO.
However, the wording for DOGSO-H does not mention anything about an offense punishable by a free kick, all it mentions is that you're sending off the player for denying a goal by deliberately handling the ball, which this substitute has done. Therefore the correct thing to do is to send the player off for DOGSO-H and an indirect freekick.