A "motion comic" is defined to be a comic like presentation of graphical content but augmented with basic animations and perhaps sound within the panels. It will ever have user interaction to advance the story and may have interaction to examine pictorially given details (to mimic the look-at / examine functionality of IF / TA / GA). Such interaction has no impact on the story.
Now, It may have interactions that leads to different story paths and endings (a.k.a branching story). This is close to the CYOA approach mentioned by alnite above. Due to the narration being done in (partly) animated comic panels, this approach consumes much time of artists and requires great attention on continuity checking. All potential endings are pre-defined, and the particular reader sees a single path through the story.
Another approach is to tell the story in parts, so that one part is published per time unit (e.g. a week). Each part ends on a branching point, and the readership is enabled to vote online how the story branches and hence advances in the next coming part. This approach to influence the story is not directly depending on the motion comic media, but it reduces the overall amount of work drastically. At the same time it has, obviously, other hurdles.
Graphic adventures (or GA for short), often implemented utilizing the point-&-click interaction style as mentioned by Alberth, are a different thing. They and their text variants TA and IF are based on a concept where the player is in a room and can examine and interact with the things therein and finally leave the room through one of the exits. Notice how different the media is. In a motion comic, the story is narrated in a sequence of panels, each one allowing to express a dramatic composition with camera settings and scene composition and such, while a GA does not do such things.
In other words, the artistic expressiveness in a motion comic is much greater, while in GA the interactive part plays a bigger role. Interestingly enough, the authoring systems available for GA can also be used to design a motion comic (although I doubt a bit that all that nice effects seen in motion comics can be done with them … but maybe).
Allowing the readership to contribute content to a story driven motion comic - well, ATM I cannot really imagine that it will work well. Can you share your ideas with more details?