You must know that this stuff was later also codified in successive (so-called hard) international human rights treaties like the ICCPR (see Article 17 in this case), right? That Covenant now has 175 parties, plus six more signatories without ratification (most notably China and Cuba) — North Korea is the only state that has tried to withdraw.
In some of those states, the provisions of the Covenant may be considered directly applicable/self-executing, having the legal force of a provision of constitutional rank, while others require some kind of national step or implementation. Whatever the case, it's arguably at the level of incorporation into national law, though, that the ICCPR has exerted its greatest impact. Basically, post-WW2, when anywhere in the world a national constitution has been framed, the ICCPR has served as the natural yardstick for drafting the fundamental rights provisions.
And beyond nation states, I'm glad we're not dependent on UN bodies and agencies for the development and enforcement of human and fundamental rights more globally either. Sure, the European Court of Human Rights doesn't have an army of its own, and part of the influence and relevance of the law it creates is a bit squishy, frankly, hinging on the authority, gravitas and respect bestowed on it by a somewhat opaque and shifting web of institutions and so on. It's certainly not nothing, though, especially since nowadays the ECHR's jurisprudence is mainlined by the ECJ basically uncut, and also applied as constitutional-level law by the rest of the eurocracy basking in the supremacy of Union law.
But I don't know, man, this human rights talk is always a bit of a gamble in terms of using your time well, at least if addressing a crowd where potentially more people support the death penalty than the ICC.