Let me explain it to you. Hungary was a Kingdom between 1000 and 1918. After the Treaty of Trianon, the Kingdom was restored but the Habsburgs were dethronemented. Lots of stuff happened between 1918 and 1920(communist takeover for a few months, Romania marches into hungarian lands etc).
So, after 1920, we needed somebody to rule. De jure we were in regency, and Miklós Horthy was our Regent. Although his title was kormányzó, but its kind of the same thing. But our nation had a parliament, had their parties, had elections. The ideology was fascist, the form of the government was a Kingdom, but we haven't had a king.
Edit:
Germany as example, their nation were fascist aswell, but they used a one-party system (NSDAP in Germany