yes, some people swap the meaning of concurrency and asynchrony. But, almost all implementations of async use main event loops, global interpreter lock, co-routines etc. and thus at the end of the day only do one thing at a time.

Therefore I think this definition makes the most sense in practical terms. Defining concurrency as the superset is a useful construct because you have to deal with the same issues in both cases. And differentiating asynchrony and parallelism makes sense because it changes the trade-off of latency and energy consumption (if the bandwidth is fixed).