Of course there is a relation here and thanks for posting this. But I think that there are other factors too in this as culture (register or not as player at a certain level/prognosis of development and dedication. I also think that other structural factors of "harder" nature than culture are hidden in these numbers.
If one index these two sets of stats you kindly posted we get this:
("1" = percentage of players equal to percentage of players i.e. equilibrium)
What this really means can not be stated without further facts, but some musings/hypothesis can be made.
Firstly, I think that there are an even bigger percentage of number of outdoor rinks in Canada than they have in indoor rinks (60% or more?). This explains why Canada is so low in the index, they got other rinks which makes up for this. The Czech can hardly find this excuse, even if there are rinks they got a pretty bad winter compared to say Finland. Perhaps this number is indicative and explains the decline in Czech hockey. Or perhaps very many register as players and do not play very much, it could be a case of lax bureaucracy (which differs very much between nations).
Well this was some thoughts, others have certainly better idea and suggestions. I just want to point out that this is more complex than what first meets the eye.
I agree there are details which could shift the percentages a few points either way, but for the most part the numbers appear to be reasonable accurate.