They're very leftist, remember that Venezuela have always been very leftist. The party that was Chávez big nemesis Acción Democrática was a former communist party that after they split from castro-comunismo they were still very socialist and always remained friends of Fidel, they are part of the Socialist International just like Voluntad Popular that's Guaido's party. Venezuela's right died in the 60s after Marcos Pérez Jimenez was removed from power by the communists.
Anyways there's a lot of bullshit information about Chávez, for starter you keep seeing everywhere that he nationalized oil and other minerals, bullshit, oil and everything under the ground was always owned by the government since Venezuela existed and even before that, then they may say he nationalized the oil industry, bullshit again, the oil industry was nationalized in 1975 by Carlos Andrés Pérez, Chávez untra-nemesis and the President he did the coup against, yes Chávez was a putschist, which is why it's so laughable that chavista are always calling everything the opposition does a coup. He also didn't nationalize our universities nor our public schools nor our hospitals and honestly he didn't do anything new that adecos or copeyanos haven't done when it comes to social programs or economic policies other than different names (like CADIVI = RECADI), price controls, import controls, big tariff, nationalizing shit, reforma agraria (taking land from big owners to give to the little guy), building housed and apartment complex for the poor, trying to diversify our economy (LOL), all that crap was done before Chávez, it just didn't work like it didn't work with Chávez.
Remember I said we nationalized the oil industry in 1975, well we became ultra rich for a few years, one of the richest (top 5) countries per capita in the world, in 1983 we collapsed and this collapse eventually brought Chávez to power 1999 because people just couldn't understand that we couldn't go back to the golden days when we were super rich and the government gifted you everything.
Well, we successfully accomplished the 50-50 without getting Iraned, we created OPEC, we nationalized our oil industry, we were always super lefty, among other things, so if that counts as being under the US thumb then I guess they're right.
For all practical purposes Venezuela's economy is completely nationalized, all the important parts of the economy, starting with oil which it's most of our economy are completely in hands of the government, then all the others are controlled by the government, like if you produce food you can't decide where or whom to sell it, there is a government office that tells you to whom and by how much money, etc. And then most of these 'private' industries are owned by government officials or their testaferros.