As far as I'm aware we've never had a nuclear reactor go sideways, and it's kinda ludicrous to even ask. It's one of the most massive structures, built on bedrock because it's too heavy to be built on anything else, and even these "small" reactors will be incredibly heavy.
From a planning perspective, if verticality is a requirement then that verticality has to be protected as strongly as any other aspect. Any attachment or mounting points that maintain verticality must therefore be earthquake proof. If, as in the pictures, these reactors are held in place from the top, horizontal shaking from even a small earthquake would put massive strain on that joint. It isn't just the long/thin/heavy reactor but all the water sloshing around too. A super-strong joint and maybe something important bends/breaks under load? A flexible joint to allow the reactor to sway? Sway how much? What happens at the travel limit of the joint? Can we risk the reactor contracting its neighbours? These are not trivial engineering questions.