There is some "random" screening just after some of the immigration check-points. But its not applied to all passengers. I have been "selected" for the check a few times. Its just carry-on bag x-ray, not any personal scan of any kind. That all happens at the gate.
The at-the-gate full screening is not unique to Singapore. Similar process is applied at KUL, but there is also a mandatory pre-screening after immigration. No screening for inbound passengers though - they just enter the combined departure/arrival terminal.
By performing the screening at the departure gate, there is no requirement to isolate arriving and departing passengers, simplifying the overall design. It also means that passengers don't get caught in a long queue for security and miss their flight.