Polymerization Isomerism In Transition-Metal Complexes Not True Isomerism?
I’m pretty sure that polymerisation isomerism should mainly be considered a historical term nowadays. Going back in the history of science, all people knew at some point was which elements a specific compound is made out of. That worked well for main group metal salts but not too well for transition metal salts. Later, quantitative analysis established the law of multiple proportions, which basically says that if two compounds are made up of the same set of elements, the ratio of element mass ratios will always be an integer ratio. Sounds hard to understand, here’s an example:

$\ce{CuCl}$ has one chlorine per copper, $\ce{CuCl2}$ has two. So for every $x~\mathrm{g}$ of copper, one of the two will have $1~\mathrm{g}$ of chlorine, the other will have $2~\mathrm{g}$, and $1$ and $2$ form a simple integer ratio.

And all of a sudden there were compounds that were clearly distinct but gave the same ratio of elements, a simple example being $\ce{NO2}$ and $\ce{N2O4}$. To understand this, the term polymerisation isomer must have been introduced.

Nowadays, isomers are defined as having the same elemental composition on a per-fragment basis. So examples such as $\ce{N2O4}$ (which is a different molecule than $\ce{NO2}$) or the platinum complexes you give would no longer be considered isomers — neither constitutional ones nor stereoisomers. Hence why so many people said ‘your second book is right.’