It looks like the original map was made in WorldPainter, which is a map generation tool for Minecraft. According to the WorldPainter site;
"When you leave the WorldPainter-generated chunks, Minecraft will start generating land again, according to the seed you specified and its own algorithms"
Once you leave the area that the map-make was working with, Minecraft should start generating new chunks like normal. The map-maker may have defined the ocean outside of the islands as being very large, however, so it might take a while to get to the new areas.