"External" clock synchronization and sbsolute motion
The clocks in the two frames have been synchronised in two different ways.
The C clocks are synchronised by an "internal" method (Einstein sync) which can be carried out in a "closed box" without knowledge of any other frames.
The C' clocks have been synchronised by an "external" method which depends on knowledge of the C clocks.
As the two coordinate systems have been set up in different ways, there's no reason why the laws of physics should take the same mathematical form in the two coordinate systems. The principle of relativity has not been broken because the two observers are not using the same method to make their calculations.
And it's not surprising that R' can work out his velocity relative to I because he made use of I to sync his clocks.