It's called a topological insulator because the flow is restricted to a surface, boundary, or interface instead of the bulk. So in the sense of a topological insulator, equatorial waves are topological boundary states, similar to those emerging in various topological insulating media according to Delplace et al. It's ok that they make these physical analogies, while I just as soon work directly with the equations and then evaluate with respect to the data.
One of the saddest correlations I have observed is the emergence of MJO cycles as traveling wave offshoots of the equatorial ENSO, delayed by about 21 days
I have inferred from reading the literature that climate scientists consider MJO as being an independent behavior, but this essentially shows the direct connection. (it's sad if no one else has observed this direct time-series correlation until now).
So ENSO is the standing wave but it has an impact off the equator either through these traveling waves or via a common-mode forcing mechanism which synchronizes standing wave dipoles away from the equator. The buzzword is teleconnection, which implies causation at a distance.