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OK, I more or less understand this and why it's so exciting, but here's my question: Is the energy output of this fusion process greater than the energy input?

I don't think they're anywhere near break-even with it. The exciting thing about this is that they've done this on a cheap table-top device which suggests it will be several orders of magnitude cheaper and easier to get energy from this process than the huge tokomaks that the multi-nation ITER will ever be able to approach.

What they are doing here, if it actually is working and not some flaw in the experimant design, involves a rate of nuclear fusion measured in countable numbers of atoms. The energy released, while purportedly real, is below the threshold of detection, and the energy density is close to zero.

To create a practical energy source, all of these would have to be scaled up by many orders of magnitude. I don't believe that energy could be extracted from such a system as anything other than heat, which means the ability to boil water to produce large quantities of high-pressure steam, continuously.

Perhaps, but that is a long way off when we are not even completely sure that the process works at all.