What kind of stereoisomerism do cisplatin and transplatin exhibit?
The definition of diastereomer does not include "requires two stereocentres" anywhere. It is simply


  Diastereoisomers (or diastereomers) are stereoisomers not related as mirror images. (IUPAC Gold Book)


Therefore cis- and trans-$\ce{[PtCl2(NH3)2]}$ are diastereomers.

(E)- and (Z)-alkenes are also diastereomers of each other. Your "cis/trans stereomer" is in fact simply a subset of diastereomerism.