You are right. I checked the source, it is the graph on slide 14 of the Lazard presentation [1]. The graph is the levelized cost of energy (LCOE) in dollars per MWh.
That is incorrect. The article is referring to the cost of the infrastructure, not the cost of the electricity that infrastructure produces. Power plants are spec'ed by megawatt (peak).
In no way is the capex of any of those options that low, not by orders of magnitude.
Dollars per kilowatt would also make more sense but yes the number are off by about a factor of 1,000. If a 1 GW nuclear power plant cost only $200 per megawatt the entire plant would cost $200,000 which is… completely wrong
Utility scale solar is around $1/W, so even $/kW wouldn't work.