Looking at this sheet music, I would have played E and G but he plays C and E. Is there something I don't understand?
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It is most likely simply a stylistic choice. The general chord this section is built around appears to be C major, so playing C and G is a perfectly reasonable (if not BETTER) choice to make. In the future, however, realize that sheet music is not an end all be all. The answer to your question is quite honestly "why not".
To elaborate a bit on Laurence's answer, there are several questions on this site concerning keyboard music that appears to call for the same note to be played simultaneously by both hands (or by one hand while the other is holding it down having already played it), so this isn't per se a red flag. In those cases, however, it's because of a desire to show that the same note belongs to two different musical ideas that happen to overlap at that point. In this case, the left hand part especially is not particularly melodic. Furthermore, the instruction "with ped" means that the G will not sound any different whether it is held as a quarter note or a half note.
In this case, as it is an arrangement, I would tend to view the original as "correct." If you listen to the soundtrack (for example in the trailer, below), you'll find that there's definitely a C in the first chord.