> Does this actually prove that antimatter necessarily exists?
Antimatter definitely exists, it is detectable, and used; e.g, PET scans use positrons (anti-electrons), and there have been experiments (only in animal models last I knew) with anti-proton radiotherapy for cancers.
This is the first evidence of a particular configuration of antimatter, not the first evidence of antimatter.
To be more specific this is the first time we have detected hyper-antimatter of Helium where one of the quarks in the nucleus is an anti-strange quark (an anti-lambda from the article)