Why non-crosswind type is not popular?

Welcome @mingaero ,

Indeed Sky WindPower is classed in rotational AWES with electricity generation on the flying device, classification on Figure 2 page 3 on the pdf (Electricity in the air: Insights from two decades of advanced control research and experimental flight testing of airborne wind energy systems) on the link on the message below:

For now it looks like crosswind devices produced more electricity during experimental tests:

Figure 15: average 92 kW, 12 m/s wind speed.