I think the organiser meant something else but if the rules were not clear at the beginning then the author in question should be allowed to continue in the competition (I am not thinking of a specific game here). If we take the rule literally (as would be the normal thing to do) then games where "you can traverse the game purely by clicking" will be disqualified. Taken literally, this doesn't make sense. If the game can be completed purely by typing, it is not becoming less of a parser game just because you can also"traverse the game purely by clicking". I think the thought behind this was that it must be possible to play through the game purely by typing (not considering obvious "press any key to continue" or "press button to start") or perhaps the organiser just meant most of the time(?). If a rule was not written as intended, a game breaking such an intended rule should be allowed to stay in the competition.
The above is about disqualification in general. Regarding "Lantern", we don't know why Sylfir decided to remove all his/her games, there can be many reasons for that. But it would be interesting to know why.