Is there a word for powerful people in politics? There has to be, I know the word "insider", but "insiders" aren't all that powerful, some are, but they are not the ones who make the decisions necessarily.
I can't think of a single word that applies to politics specifically, but you could make use of magnate:
: a person of rank, power, influence, or distinction often in a specified area
// a railroad magnate
Since it could be true of any field, a qualification is necessary:
She was a political magnate.
From Wikipedia's entry on George Maitland Lloyd Davies (emphasis mine):
Davies was born in Peel Road, Sefton Park, Liverpool, grandson on his maternal side of a noted Welsh preacher, John Jones, Talysarn; his family was wealthy - his cousin was David Davies of Llandinam, a Welsh industrial and political magnate.
From "5 Surprising Facts about the Patty Hearst Kidnapping Saga" by Randy Dotinga (emphasis mine):
Terrorists had kidnapped Patricia Hearst, the young granddaughter of newspaper and political magnate William Randolph Hearst, and no one knew what chaos would come next.
From "The Percy Family, Marching with English History" by Dean Smith (emphasis mine):
Henry, 4th Lord of Alnwick soon became Edward’s most important courtier (and political magnate). In 1377 Henry Percy was Marshal of England, and then Earl of Northumberland.
"Powerful politicians" and "abusive politicians" (where it can be implying some considerable to significant degree power that can be abused). In benefits / qualities it is pretty concise (short) and also associativity descriptive and simple for common understanding. Because of those benefits it can be relatively better term than both 2-words alternative/option terms for this and also even some, I'm not sure if they are existing, 1-word option terms for the meaning because it's still pretty short and okay (as opposed to if it would be 3/4/more words) and also have mentioned other benefits