Well, as I’ve commented above, I don’t know if Egnor himself understand Aristotelianism properly. Still, what Egnor is saying here is just repeating a common narrative among Thomists. As a physicist I would disagree that final or formal causes exist in physics today. The main concern of modern physics is to provide an equation that accurately characterizes the evolution of any physical system. Physics is agnostic over what “causes” the equations to be true - for that we need to get into the philosophy of science (see: What are Laws of Nature?). As Feynman said, the modern physicist’s main preoccupation is to “shut up and calculate”. So even the fact that these sorts of discussions are held among philosophers, not physicists, is a sign that modern physics is primarily concerned with only material and efficient causes.
Now going specifically into philosophy of science, even if you believe in something like OSR (which @BruceS mentioned), where everything at the very bottom is just mathematics, it would be a stretch to say that these equations would be the same as Aristotelian formal causes.
Regarding final causes: I’m not a biologist, but I very much doubt that true final causes exist in biology. I thought this is why ID is so controversial, though - remember those debates we had with Eric Holloway about teleology? (But it’s important to remember that ID proponents are generally not Aristotelians either.)
Final causation is even less important in physics. Aristotle believed that even a stone falling to the ground exhibited a final cause. This statement is meaningless in modern physics, since it is not something which is experimentally testable. Modern physics adopts a pragmatic philosophy of verificationism, where something is only of scientific interest if it creates a difference in observable quantities.