Yes it is the rudder shaft if it spins freely at rest but binds when there is a horizontal load (even just at idle). I'm not familiar with whether your model has a grease fitting on the rudder shaft. Just hitting it with grease may lube it up enough. In my case it only made it marginally better for a very short time. Old grease had hardened on mine so I dropped the rudder, cleaned the shaft and housing. Grease it annually.
2003 ProStar 209, 2 flags, 8 cup holders