Specificity plays an important role in "strength".
In the quote you provide, the point that Rippetoe is making is that back squats, conventional deadlifts, and overhead presses with a barbell are much more similar to the sorts of moving one does in every day life than things like seated leg extensions, hamstring curls, and cable lateral raises. Rippetoe explains this more clearly in the paragraphs after your quote:
Properly performed, full-range-of-motion barbell exercises are essentially the functional expression of human skeletal and muscular anatomy under load. […] Barbells allow weight to be moved in exactly the way the body is designed to move it, since every aspect of the movement is determined by the body.
Machines, on the other hand, force the body to move the weight according to the design of the machine.
To the extent that a particular "every day movement" is similar to one of those barbell lifts, he is absolutely correct. Barbell overhead press does better prepare you for lifting objects above your head than some sort of deltoid isolation movement or combination of isolation movements, because specificity, that is, the similarity between the movement we train and the movement use to measure strength, is very important.
A 2018 study by Rossi et al examined the effects of squat and leg press training on squat and leg press strength. The full study can be had at that link, I'll summarize the design and key results here.
Subjects were randomized into three groups:
- A squat only group (SQ)
- A leg press only group (LP)
- A squat and leg press hybrid group (SQ-LP)
Groups trained twice a week for ten weeks with six working sets per session. Squat and leg press 1RMs were tested before and after the ten week protocol, and here is my summary of the results (Table 2 in the paper):
||Squat 1RM % Increase
||Leg Press 1RM % Increase
All three groups showed similar increases in leg press 1RM strength, but the SQ and SQ-LP saw much greater improvement in squat 1RM than the LP group. Essentially, to improve your squat you need to squat. The key observation here is that the more complex a movement is, the more important specificity of training becomes. The leg press is a very simple movement: the weight is on a track and does not need to be supported with the musculature of the trunk. And of course, there is a lot more going on with the squat, being a free weight exercise carrying the weight on the shoulders.
Bringing this back now to Rippetoe's point, the movements of every day life are rarely as simple and well controlled as a leg press. Instead, we most often see more complex movements closely resembling the barbell lifts. So based on the evidence, the barbell lifts or more likely to better prepare you for the movements of everyday life than isolation lifts. That is what Rippetoe is trying to say there, and the evidence supports the idea quite well.
However, Rippetoe’s overall view of specificity (as outlined in his other book Practical Programming) leaves a lot to be desired, so I will instead direct toward Barbell Medicine’s three part article series: