Everyone else's computing time is wasted, in the sense that all that electricity and processor time (both of which cost money) have not contributed even one bit to the blockchain.
The point of the article (and I'm surprised that it takes them so long to explain it) is that regardless of the blockchain building process you choose, the entities responsible for adding blocks to the blockchain form a highly competitive market, and in these kinds of markets the costs grow very close to their expected income.
For Bitcoin, those entities are the miners, and costs grow because if you don't buy the latest high-powered hash-nozzle, your neighbor will, and your expected revenue will drop. It's an arms race that only stops once the costs exceed the revenue, meaning that most of the revenue from each block dissipates into electricity and hardware, and the electricity and hardware that doesn't contribute to a block is waster.
But even for a different blockchain model, designed to not waste anything, the same thing would happen: block-adders are incentivized to spend as much money as possible to increase their slice of the pie. In the end, the same amount of money (the revenue for a block) would still be spent in electricity, hardware, bespoke lava lamps or golf sessions with senators, anything that lets miners get one step ahead in the arms race.
Of course, if you were to drive down transaction costs, the available revenue for each block would go down, and the amount of wealth that can be wasted would decrease as well.