On any centralized exchange you're trading just numbers. Those are real coins only at depositing and at withdrawing, when they are visible on the blockchain. All the rest is numbers in the exchange's internal database.
Yeah, in additional, trading derivatives like future and option enable us to trade any underlying asset such as bitcoin, but not necessarily ownership. Because an investor is not buying or selling the asset itself but the contract that gives the holder the right to buy or sell the asset at a later date at a predetermined price. This allows traders to speculate on the future price of an asset without actually owning it.
True it is the contract to buy or sell the asset they are trading and not the actual asset. I do agree that as long as Bitcoin is not sitting in your wallet, that BTC is not yours yet.