Turkey wants to make sure the island is never used as a base from which to attack it. Though that kind of thinking may be outdated you have to remember this is a country that was occupied from all corners less than a century ago.
For us Turkish Cypriots, we want guarantees as a last resort, as a detterent should the Greeks of Cyprus, or fanatics among them, feel the urge to use their numerical superiority against us.
The point about Russia and China is they have nothing to gain by being guarantors for Greek Cypriots, the island is of little strategic value to them and they would never use any of their resources to protect something which does not benefit them in some way.