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I think seeing the people behind the conspiracy as bigger than they really are is exactly playing into their hands.
Literal
That conspiracy [object-を] are-plotting people [object-を] necessary-more-than-に big-[adverbial-く] end-up-seeing thing [topic-は], exactly their [genitive-の] thinking-pot is [quotative-と] think.
Conspiracy-theory-skeptical commentary with a memorable idiom. 思うツボ is an idiom literally 'thinking pot/trap,' meaning 'exactly what X wants,' 'playing into X's hands,' 'falling right into their trap.' 思う + 壺 ('pot, trap for fish or birds'), evoking the image of being lured into a trap set up by someone. ~てしまう ('end up doing,' with regret) marks the overestimating as an unwanted outcome. 必要以上に ('more than necessary') is a set phrase for excess. 画策する ('to plot, plan, scheme') is a formal verb for deliberate planning, often negative (conspiracies, schemes). The whole sentence is a counsel against falling into the rhetorical trap of granting too much power to conspirators.