He wasn't king, he was "regent" - one who stands in for the king.

After the chaos of the immediate postwar period, with the Communist "Red Terror" and the reactionary "White Terror" the Hungarian assembly decided to reform the "Kingdom of Hungary" with the last Austro-Hungarian Emperor, Karl I, reigning as Karoly VI and Horthy with the army behind him was able to be declared regent in his absence. However, not only were the Allies deeply sceptical about allowing Charles to reclaim part of his kingdom, but Horthy himself wasn't keen on the idea either (depending on who you asked, either out of personal ambition, or because he knew Hungary would probably be invaded if the king returned). So he maintained the position of Regent, while making sure the actual King could never return.

I've never seen a link suggested in any serious scholarship, but the parallels with Denethor in the Lord of the Rings series are striking, particularly given the time frame during which the books were written.

Being a Fascist State doesn't mean a nation couldn't be a Kingdom, in fact Fascist Italy was both a Dictatorship under Mussolini AND a Kingdom under the reign of King Victor Emmanuel III