What kind of stereoisomerism do cisplatin and transplatin exhibit? Cisplatin and transplatin are obviously isomers, more precisely stereoisomers. Now, they aren't chiral, so they cannot be enantiomers. They cannot be diastereomers either since they don't have two stereocenters. They don't belong to cis/trans stereomers either since they are a subgroup of diastereomers and again require two stereocenters. So - what the heck?
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.