I largely agree that the human impacts of earthquakes are greater in poorer countries, although the picture depends on the type of impact measured.
There is strong evidence that social impacts are worse where countries are poor. The Haiti 2010 earthquake (M7.0) killed an estimated 220,000-230,000 people and left around 1.5 million homeless, and a later cholera outbreak killed thousands more. This was not because the quake was unusually strong but because Haiti is a low-income country: weak building codes meant homes pancaked, there was little preparedness, and the under-resourced emergency services could not reach survivors quickly. A powerful comparison is Chile 2010, which struck the same year with an M8.8 — far more energy released — yet killed only a few hundred people, because Chile is wealthier with enforced earthquake-resistant building codes, drills and a fast response. This shows vulnerability (wealth, building quality, preparedness), not magnitude, drives the death toll, supporting the statement.
However, the statement is too absolute. If we measure impacts by absolute economic cost, richer countries can suffer more because they have far more high-value infrastructure to destroy. The Tōhoku (Japan) 2011 earthquake and tsunami (M9.0) caused an estimated US$220+ billion of damage — the most expensive natural disaster on record — and forced the Fukushima nuclear shutdown, even though Japan's excellent building standards kept most deaths to the tsunami rather than collapsing buildings.
Overall, I agree to a large extent for human and social impacts — deaths, homelessness, disease and slow long-term recovery are clearly greater in poorer countries such as Haiti, because vulnerability rather than magnitude determines loss of life. But for absolute economic impact, richer countries like Japan can lose more. The fairest judgement is therefore that the statement holds strongly for the human cost, but not for every type of impact.