So, I went little deeper into this issue... I've communicated with Kawasaki regional HQ directly. My bike seems perfectly OK - everything is as it should be. HQ tried their own Z900 and it wanders to the right as well. Dealership's Z900 is doing it as well, although it is a little bit better because it has lighter exhaust on the right side (Akrapovic).
Conclusion is that it's not a bug, it's a feature. When I look at the bike from behind, rear suspension is tilted to the right and exhaust is on the right side, so it's kind of logical for me - right side of the bike is heavier.
This can be corrected by slightly tilting a rear wheel axis (moving right axis screw slightly back), because rear wheel behaves like a rudder of the ship. Tilting each 0.5 mm makes a difference. However the guy from HQ warned me that tilting the axis even 0.5 mm might cause the bike to misbehave in high speeds.
So I left it like this - wandering is pretty small and only when I release handle bars. When riding normally I cannot feel any wandering whatsoever. And in high speeds bike is totally fine.