If the question were the other way 'round - "If I add a railing on the side closest to camera, would I need a railing for the little gap on the far side" would make far more sense. However, in both cases the answer is "Yes", you need railings on both sides.
I don't know what the exact code references are, but logic dictates. You might be single or newly married, but I guarantee that once you've got a toddler climbing up and down the stairs, you'll fully understand why you need a railing on the near side, protecting that large gap. Even though the far side gap is smaller and the drop shorter at only 4 steps, that's a long way for a 2-year-old to fall and land on her head.
If you want to minimize the viewing obstacles, consider:
A glass railing. It'll cost, and it may cut down sound transmission. Reducing the sounds going upstairs might be good, but it may negatively impact conversation across the stairs.
A cable railing - it won't have the sound deadening issue, but the thin cables will still allow for a mostly unobstructed view across the stairs.
I do know that (US, at least) code requires that balusters be no more than 4" apart to prevent small children from pushing their heads through and getting stuck.