Are these options 'special'? Is the standard pricing models applicable to them?

Good link. That's the kind of situation that was a possibility. 
I am just wondering how volatility (any..) models will lead to realistic prices.

If the option price is bounded on a daily basis does this fact not screw up stochastic models and assumptions? Has a sacred rule been transgressed?

Agree -- good paper. 

However, the authors define an "implied interest rate" as one that enforces put- call parity in the absence of dividends. Hard to interpret, IMO.

It it might make more sense to interpret "hard-to-borrowness" as a (maturity-dependent) dividend rate [$]q_T[$] (longs receive, shorts pay). This is essentially how it actually works for large (institutional) investors in the US when they borrow/loan stock. So, you don't alter the riskless rate [$]r_T[$], but alter the dividend rate. In principle, with this adjustment then "standard" (PC parity-preserving) theory/models can then be used normally.   

A little googling suggests that  stock lending in China is still in a very primitive state relative to US model. Nevertheless, their option markets might still be behaving "as-if" there was indeed a well-defined [$]q_T[$]. In any event, it's a testable assumption.