A clear term describing the measurement method of the "sampling oscilloscopes" discussed in the linked article would be "equivalent- time sampling". "Sampling oscilloscope" is a short cut, a bit ambiguous at times when most general purpose oscilloscope on the market are real-time sampling oscilloscopes.
I can just guess that the OP is specifically referring to equivalent-time sampling, but not sure about. Eye diagrams can be well acquired with equivalent time sampling, however.