AFAIK the Owner's "earlier rights" refers to the fact that the Owner has filed for/registered a Trademark before someone else did, so to me "earlier" seems correct (it is about the chronological order, first to file, rather than some hierarchy)
Well, "earlier" is undeniably ambiguous. Does the Owner still own those rights or not? If not, then there would seem to be no reason for, or purpose in, the Applicant's acknowledgment of those earlier rights (the rights the Owner owned at some earlier time).
Maybe Applicant is acknowledging that it has no trademark rights in the EU, because the Owner has those rights. In that case, I'd refer to the Owner's existing rights, not its earlier rights. Earlier suggests that the Owner had them once (at some earlier time) but no longer.
On the other hand, if Applicant is somehow sharing under the Owner's rights (i.e., the Applicant has certain rights under the trademarks, subject to the Owner's superior rights), then I'd call that a case of the Owner holding the senior rights, with Applicant holding junior rights.
Maybe "senior" is not the best term in this context (maybe "superior" is?), but I cannot see how "earlier" works here without being ambiguous.
I had not seen #14, and I know nothing about EU-English, but apparently EU-English is short for ambiguous English.