The concept of ordering is independent of architecture. What operations need to be ordered relative to other operations to be correct does not change. But, your architecture may implicitly guarantee certain orderings so you do not need to explicitly guarantee those orderings.

If I remember correctly, x86 basically gives you everything except S-L automatically. That means a traditional acquire, L-LS, and traditional release, LS-S, barrier should be "free" and require no explicit instructions. I forgot about that, so it makes sense why they would not mention the presence of explicit barriers. But, that does not change the fact that you need that ordering to guarantee correctness, it is just built-in and automatic.

The oddity here is that speculative loads across a L-LS ordering requires some pretty deep black magic to be going on at the hardware level. I have no idea how they could safely reorder stores across a L-S ordering and still maintain "as-if" the store happens after the load, and even safely reordering loads across a L-L ordering and maintaining the "as-if" seems pretty arcane. The fact that the paper is claiming their PoC works and thus the reordering must be happening is wild. Either the processor is not correctly implementing the declared memory ordering semantics, or they are doing some real reordering magic.