Yes - Israel used this rather famously on ex-Nazis that they "extralegally imported" from around the world, even though a) the accused was not an Israeli citizen, b) none of the victims were Israeli citizens at the time of the crime, c) the crimes did not occur on Israeli territory. In most other cases those would be major jurisdictional issues.

Nit: Kissinger was actually tried as a war criminal in Spain under the principal of universal jurisdiction. Assuming he did not visit Spain he was immune to actual punishment, of course, but "winning" did not make him immune to being tried under that legal principal.

That’s cool. I think I’ll try Tony Blair as a war criminal tomorrow in my bedroom. It’ll have the same practical effect.

That's how sovereignty works. You can enforce laws in territory you control.