The older WIZ820io needed a reset pulse. It would not work at all without the reset pulse and would even interfere with other SPI chips. That older W5200 chip could be used without the shield, but it needed either a reset circuit (as on the shield) or a pin to pulse the reset signal.
Thankfully the new W5500 chip fixed those problems, so you don't need the reset circuit or a reset pulse, though it certainly doesn't hurt. You can just connect the WIZ850io with wires.