You're not really contradicting o11c here; what LLVM calls "environment" is a mixture of what they called libc/abi/fabi. There's also what LLVM calls "subarch" to distinguish between different architectures that may be relevant (e.g., i386 is not the same as i686, although LLVM doesn't record this difference since it's generally less interested in targeting old hardware), and there's also OS version numbers that may or may not be relevant.

The underlying problem with target triples is that architecture-vendor-system isn't sufficient to uniquely describe the relevant details for specifying a toolchain, so the necessary extra information has been somewhat haphazardly added to the format. On top of that, since the relevance of some of the information is questionable for some tasks (especially the vendor field), different projects have chosen not to care about subtle differences, so the normalization of a triple is different between different projects.

LLVM's definition is not more or less correct than gcc's here, nor are these the only definitions floating around.