Equal Earth preserves relative areas after rotation too. Shapes and directions can change.
Why does a world map centered on Australia look so different? What does the center point mean?
We choose a point on the country's main land component using Natural Earth data at 1:50 million scale. For Tuvalu we use the approximate location of Funafuti. This is a view anchor, not an official geographic center. Small islands may have no visible outline on the simplified map, but their marker still shows their location.