Latin America: No. The Monroe doctrine and the rapprochement between Britain and the US. If the largest navy in the world was willing to support the Americans against other European powers there is no room for any Great Game in Latin America.
The Ottoman Empire was still intact, even though it was crumbling. It would certainly not have been an easy land grab, and if anyone had tried, the Ottomans would have been able to ally other European powers. And the Europeans wouldn't be able to agree how to split it anyways.
China: Well it happened OTL. I don't think it could have gotten any worse for them.
Spanish/ Portuguese/ Dutch/ Belgian colonies: Perhaps. It was the abilities or inabilities of the minor colonial nations to ally with larger powers that decided their fate.