Whatever it exactly is that happened to him, it probably also happened to Michael and Walt.
Lisa Gellhorn is brought back to life by The Island as a reward for Elliott learning the lesson it was teaching him, and finding his "way home". The Black Smoke does come face to face with Elliott and chooses not to kill him, presumably because he is on his path home.
Elliott was exposed to intense radiation behind the Swan wall, just like Desmond was. When he left the island, he experienced symptoms similar to Desmond in "The Constant", except he's switching between parallel universes, instead of points in time. (There are no parallel universes on the show, but the game is not 100% canonical.)
We do not know if parallel universes will make an appearance in the show. One of the stories included in the Mystery Tales that appears in "Cabin Fever" relates to time traveling to "futures that might have been".
Well it did happen. There's an alternate dimention. But what could've happened is an earthquake, (which would explain the shaking) which threw Eliott's boat offcourse. (Which would explain the flash)
Elliott was (secretly?) modelled on a background cast member, specifically Rolf Smith.
The reason Elliott went back in time at the end of the game is to let you know that Elliott's role on the island affected the past and also that he is not only still on the island but in fact on of the survivors that we know lived and still occupies the island.
This could be due to the recently descovered Flash-Sidways timeline.
Elliott never ended up appearing in the flash sideways.
His name was spelled quite unusually. It is possible that it is an anagram, knowing the creative staff's penchant for anagrams. "Allow Lost Time" is one possibility, possibly a reference/joke to the time spent playing the game.
In the original timeline Elliot and Beady Eyes board Flight 815 and crash. The events of the game do not follow the events of the show because this is the wrong timeline. In the second timeline, Lisa boards Flight 815 in place of Beady Eyes and is present in the timeline present in the show.