But they explicitly state, on the site, that they measure "Left-Right" by just economics (not socioeconomic), and "Libertarian-Authoritarian" by just social (not sociopolitical), and the whole grid is political. They explicitly explain that, it is not just my interpretation.
Direct quote from the site: "Left---Right: If we recognise that this is essentially an economic line it's fine, as far as it goes. We can show, for example, Stalin, Mao Tse Tung and Pol Pot, with their commitment to a totally controlled economy, on the hard left. Socialists like Mahatma Gandhi and Robert Mugabe would occupy a less extreme leftist position. Margaret Thatcher would be well over to the right, but further right still would be someone like that ultimate free marketeer, General Pinochet. That deals with economics, but the social dimension is also important in politics. That's the one that the mere left-right scale doesn't adequately address. So we've added one, ranging in positions from extreme authoritarian to extreme libertarian." They are dismissing the social implications of left-right ENITRELY, and only measuring social policy according to the other axis. So even by your own logic, their system is flawed. What you KNOW about politics and what I am saying about them are in line. The site's own description and methodology are what is flawed, as you should easily see based on what you just wrote. Unless you are going to disbelieve what they say about their own graph, and assume they are measuring it correctly despite the fact that they explicitly state they are not.