Firstly, "Evolutionary Arms Race" is not tautological, it is a specific term of art in evolutionary biology.
Secondly, "evolutionary arms race" is a correct answer, it is the general case of which the Red Queen hypothesis is a special case. I do agree with you that OP described a Red Queen case, though I would hesitate to say it was because of "equilibrium"; many species in Red Queen situations have in fact gone extinct.
Firstly, "Evolutionary Arms Race" is not tautological, it is a specific term of art in evolutionary biology.
Secondly, "evolutionary arms race" is a correct answer, it is the general case of which the Red Queen hypothesis is a special case. I do agree with you that OP described a Red Queen case, though I would hesitate to say it was because of "equilibrium"; many species in Red Queen situations have in fact gone extinct.
https://en.wikipedia.org/wiki/Evolutionary_arms_race
https://en.wikipedia.org/wiki/Red_Queen_hypothesis