They are proposing that researchers need to re-examine the assumption, specifically within cognitive training research and literature, that targeting domain-specific skills ("mental abilities that are engaged only when material related to a particular field is involved") also impacts domain-general skills ("mental abilities that are used to solve complex tasks regardless of their content"). This is not the same as saying cognitive training (and therefore schooling) is useless. Here's an except from the paper (emphasis is mine):
The impossibility of enhancing GCA by training does not imply that human cognition is not malleable to training (see Outstanding Questions). Rather, it must be acknowledged that the benefits associated with training are limited to the trained tasks and, sometimes, similar tasks. Our conviction is that cognitive-training programs should not be utterly abandoned, as long as the claims and expectations about the benefits do not go beyond what has been empirically verified.
This is a critique of how researchers are explaining and generalising the results of their studies that look at cognitive training and general intelligence, and which theories researchers should be leaning into. They are merely suggesting research needs to go into the direction of understanding where experimental results sit ecologically instead of assuming their ecological impact.
This would be along the lines of suggesting someone who performs well in their specific subject tests does not necessarily mean they are going to perform well on an IQ test (or the GAT), but only that the skills specific to these domains and subjects are being improved.
The researchers do not say this is necessarily a bad thing, even suggesting future research into how
wide and multiple domain-specific training might translate into domain-general improvements and then maybe even ecologically into the real world. They propose that training/testing
one domain-specific skill may not be an accurate assumption or representation of how this impacts and relates to domain-general skills. This would be like saying training the skills in one subject may not translate to GAT performance improvements, but training various skills in multiple subjects might.
Even with all this, the debate between is so far in that research is pointing to a mixed explanation like we've more accepted a mixed explanation of nature v nurture.
Domain-general skills also can more broadly exceed cognition-focused ideas, and cover things such as teamwork or organisational skills which you can take to unique and novel situations - these were very much developed (in my experience at least) back in secondary and even today.