If you think about what employment means in the context of labor and wage earning, until the early 1900s, most in America would now be counted as unemployed, since they were rather "employed" in agriculture and domestic work, neither of which would be counted as a living wage today. In addition, most women, a large part of today's workforce, did not actively participate in the labor pool (looking for full-time employment as the BLS cites for employment), however that drastically changed in the 1960s and onwards.
As such, the current definition of employment is rooted in the realities of where employment was in the early 1900s. Today's definition might not jive with what the Axios article is stating, but what the Axios article is stating is not really about Employment, but rather about Income generation.
The notion of generating income must be separated from the idea of full-time employment. In the gig economy, side hustle world, most gig workers would not be counted in the employment rolls. As such, do the employment numbers matter and do we need something distinct to measure what Axios is stating here, which has more to do with income earning than full time employment?