The conditions are not really conducive to faster development; but neither are they implying with certainty a slower development.
Earth has 30% land, 70% water; you are asking about a world having six times less land than Earth. However,
Of Earth's 30% land, only about one third had strong contributions to the mainline history (most of Europe, northern Africa, south-western, southern and eastern Asia); the bulk of Africa, the Americas, Australia, about half of Asia did not really participate in mainline history until well into the Industrial Revolution.
Even if a large part of Earth's landmasses did not participate to mainline history their resources were important: consider the silver from the Americas, the gold and ivory from Africa, the wood and rubber from South America.
500 000 km² is not shabby: Great Britain (whose role in the Industrial Revolution was decisive) has 200 000 km²; Greece (where science and technology and philosophy and mathematics and logic all began) has 100 000 km², of which about 3/4 on the mainland and 1/4 on many islands; Italy (which is separated from mainland Europe by the Alps, which made pre-industrial commerce be practicable only by sea) has 300 000 km².
In mainline history civilizations developed in the temperate / subtropical zone; it may be the case that natural abundance in the tropical zone provides for lower incentives to develop science and technology -- and tropical deserts make it impossible.
I think that on a world such as that described in the question civilization will probably develop at a slower or even much slower pace than on Earth; however, probably does not mean for sure. It may well be the case that they developed faster, although this is less probable.
Consider also the incredible sheer historical luck required for human civilization to reach its current level. First there were the Sumerians, who invented a form of writing and established the basic idea of a state; then came the Akkadians, who, instead of killing all the Sumerians and burning all the cities, learned to write and continued the civilization; and then the Assyrians, and then the Babylonians, who made the first great steps in mathematics and astronomy; when the Greeks opened their eyes and learned the (easier) writing system of the Phoenicians, the Babylonian civilization was old and dying, but the Greeks learned the basics of mathematics and astronomy and carried on and made their own crucial contributions; and when the Hellenistic civilization was getting old there came the Romans, who instead of killing all the Greeks and burning the cities learned the language, and mathematics, and logic and philosophy and physics and medicine and then made their own crucial contributions; and when Rome fell there came the Arabs, who translated the books and kept the torch lit for eight centuries, until Europe woke up and translated the books and learned...
Modern science and technology are the result of many — eight, maybe nine, maybe ten — civilizations successfully passing on the accumulated achievements to their successors. This is pure luck. So maybe on your planet they got lucky earlier. Not likely, but then not impossible either.