You can have concurrency without parallelism per the definition of the article - on a single processor system with timeslicing, for example.
SIMD systems effectively give you parallelism without concurrency - only one instruction is executing, but it's operating on multiple dataflows.
Your linked definition of "concurrency limited" seems to refer to utilisation. In the scenario described, how effectively the processor can be utilised depends on how many concurrent tasks it has in progress so it has something to do while one of them is waiting for a cache miss.
Comments
You can have concurrency without parallelism per the definition of the article - on a single processor system with timeslicing, for example.
SIMD systems effectively give you parallelism without concurrency - only one instruction is executing, but it's operating on multiple dataflows.
Your linked definition of "concurrency limited" seems to refer to utilisation. In the scenario described, how effectively the processor can be utilised depends on how many concurrent tasks it has in progress so it has something to do while one of them is waiting for a cache miss.