They meant algebraic in the sense of https://en.wikipedia.org/wiki/Algebraic_operation.
> ... very becoming-numerate generation invests enormous effort in the painful calculation of the lengths and angles of complicated figures. Surveying, navigation and computer graphics are intensive users of the results. Much of that effort is wasted, Wildberger argues. The concentration on angles, especially, is a result of the historical accident that serious study of the subject began with spherical trigonometry for astronomy and long-range navigation, which meant there was altogether too much attention given to circles. ...
> Having things done better is one major payoff, but equally important would be a removal of a substantial blockage to the education of young mathematicians, the waterless badlands of traditional trigonometry that youth eager to reach the delights of higher mathematics must spend painful years crossing
Whether that's correct is different. https://handwiki.org/wiki/Rational_trigonometry seems to give a good description of opposing views.
If "formal verification" involves using a software-based proof assistant or automatic theorem prover then perhaps that easier to encode for those tools via rational trigonometry?
Why not ask him directly?
In contrast, arithmetic on rational numbers can be implemented exactly; at least, up to the memory limits of the machine (e.g. using pair of bignums for numerator/denominator)