Non-determinism is not concurrency either (I think the author is wrong to conflate the two).

Parallelism is a physical, hardware, implementation of concurrency. VLIW, vector operations, GPUs etc. execute very fine-grained operations in parallel, but whether this is regarded as concurrency in any given context depends on how "lumpily" you define a concurrent task for that particular context. For example, fancy parallel instructions might be used to resize images in a thumbnail generator in a web server, but if the task being considered is the processing of a web request, then there is no concurrency. If the task being considered is processing a line, stripe or block of pixels, then there is concurrency.