[Nagoyankee]

There's no semantic difference between the two. It's more of a matter of phonetic aesthetics than anything. There are both on-lovers and kun-lovers in this country as someone as advanced as you may have noticed.

When the word 傀儡 is combined with another compound that is read "on", however, the 傀儡 part is likely to be read "かいらい" as well for the sheer sound balance. 傀儡政権 in the article is the best example of this.

The single exception that I can think of to this phonetic interchangeability is when 傀儡 is used to refer to a female puppeteer who also served as a prostitute. Only the kun-reading "くぐつ" applies there.