This question exists in a discussion about the best power meter because Zwift is a power based system. Your character moves forward depending on how hard you push on the pedals and that means a power measurement. For many people this is the introduction to using power measurement on a bike and if you are thinking about using Zwift, understanding the requirements is a good place to start.
The simple answer is that you do not need a standalone power meter to ride on Zwift. You do need power measurement though. Luckily, most modern direct-drive smart trainers, especially those on our best smart trainers list have power meters built in, but if you use a trainer without a power meter, you need one that has Zwift compatibility. What that means is that the Zwift team has mapped the resistance curve of the trainer. That information, in combination with a cadence and speed sensor, can fit into a formula that Zwift is able to solve backwards.
The result will be a relatively accurate power measurement tool and you can ride in Zwift with only that.