To answer the question as literally as possible, if you reuse heat from a process in order to raise the temperature of something that needs heating, you are reducing waste heat.
Here's an example, unrelated honestly to the article but just your question -- you have a pan of water on the stove, and you are continually pumping room temperature water into it. You are also continually pumping heated water out of it. This is analogous to a lot of chemical reactors but to keep it simple.
If instead you run the hot water being pumped out next to the water being pumped in, the heat can be moved from the hot side to the cold side. That means less energy is needed to heat up the water coming in, because it is preheated.
So, in practice, you do indeed release less heat energy because less is required to keep that kettle hot. The hot water being removed gets cooled down some too, for better and worse (often this is good, who wants hot chemicals right?).
This has nothing to do with the article though, which is talking about using a neural network trained to help speed up predictions of phonon dispersion relations, which is great but maybe a little unclear. A phonon is sort of a quanta of heat if you like, so knowing how they travel in a material certainly is important and objectively cool, but the 70% thing does feel like a bit of a non-sequitur.
To be honest I suspect the first sentence and second are not as related as they are implied to be, the first is simply true and the second is also true but is hardly the reason the overall industrial base of humanity is only 30% efficient. Some stuff just can't be 100% efficient, like a Carnot engine. I'm shocked it hits 30% considering thermal power stations are a major thing [1]. But I also doubt materials limits make a thermal power station less efficient by much, there's just a limit on a thermal engine.
[1] To be clear, there is no citation in the press release to explain the source of this claim. Maybe it is only including after electricity generation, or maybe it only applies to industrial facilities, or maybe they're doing some weighted average of the efficiency of different electronics. I am assuming the 70% includes generation losses.