Hi there,
This is indeed an interesting question which is probably relevant for quite a lot of users, so I am happy to provide my perspective on it:
From the experiences of coachees of mine across different companies and regions, it seems that you also have to conduct the problem solving games, depending on your seniority. For instance, you will most probably not be asked to conduct them if you are already a partner with your current employer, but I fear you will have to for most other roles.
In case you want a more detailed discussion on how to best prepare for the upcoming problem solving games and interviews as a senior hire, please feel free to contact me directly.
I hope this helps,
Hagen