This is a difficult question. The term 'original' needs to be put into context. Original meaning origins would mean that this list would be populated with the first games of each genre. They were completely original, or, in fact, the very first video games full stop. But if you take original into the context of today's gaming market, say 2005 and forward, you're looking at an entirely different definition of original; where the new concepts and technologies being implemented need to be taken into consideration over graphics, story and premise. If we are looking at the first definition, then the first FPS is original, but not in today's market it isn't. Even take for example Max Payne, the first game to use bullet time, back then the slowing mechanics were original but now its in every shooter imaginable.
All of that said I would like to put forth Lost Vikings as my choice. I consider it original because it was team, puzzle platforming in way that wasn't done before at the time. It implemented a good sense of humor including overtly making fun of the user. Its premise was Vikings who were lost in time and space, each with their own puzzle-solving abilities to bring to the table. It was unique for the time and hasn't had a game quite like it (unless you count its sequel) ever.