Do you "need" the 2nd battery.... no. Since you're asking about Dual batteries I assume you have a 7.3 not the 6.7. Should you "have" a dual battery setup.... it's a "nice to have" as it provides a larger reserve of 12V energy for the winch to drain AMPs from. Depending on the winch and the load you're pulling, a winch can suck power at a rate of 400+ AMPs and if you're talking about the factory battery, it can be drained quite quickly and get damaged if not careful with the winch. Anyways the 2nd battery gives you a larger energy reserve which in theory doubles the time available for winching.
That being said another thing to consider besides a 2nd battery is having a higher output alternator. A higher output alternator can refill the energy reserves faster than a stock output alternator. When performing high amp draw winching for extended periods of time it's possible to take battery levels so low that you can damage a battery to a point where it will never get back to a full recharge cycle.
When winching - Best case scenario is to have as much alternator charging available and energy reserves as possible. For example - the 6.7 w/ the Dual Alternators and Dual Batteries provides a better setup for winching because of the high AMP output of the alternators to recharge the batteries and the dual batteries provide plenty of energy reserves. For a 7.3 you can add an aftermarket dual battery setup and probably change your OEM alternator to a higher-amp aftermarket alternator however adding a 2nd alternator to a 7.3 is probably more hassle than it's worth.
But do you need a 2nd battery?.... No. it will still work, just for less time. Just be careful and try not to discharge your battery below 50% as it might never recover back to 100% charge. Some aftermarket batteries are better suited to large high-amp draw loads and can recover from repeated low voltage situations.... those batteries are typically more expensive that OEM batteries but that's because they're specialized.