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"stretching the limits of current human capacity - but not exceeding them"

That means "feasible".

As for inexpensive, it may be a poor word choice, but the alternative is launching rocket after rocket in to space, which is one of the most expensive things humans do.

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This is not an alternative to a rocket. It goes from geosynchronous orbit height to the moon, so you still need a rocket from earth to the elevator.

It enables the use of smaller rockets rather than no rockets. With a probably optimistic ~billion dollar pricetag for something able to move 100kg. You would need to launch an awfully large number of rockets with tiny payloads to the moon for this to be a net cost savings.

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