1982 KZ305 front sprocket installation

I’m putting my KZ305 back together after having it apart for years and partially rebuilding the engine. I’m trying to get the front sprocket on, and it doesn’t seem right. The manual doesn’t show anything like what I’m working with, and it doesn’t seem to fit right. I’ve attached a video for further explanation. The manual shows the sprocket being held in place with a large nut and flat washer, but mine only has a plate that bolts to the sprocket.

I didn’t mean to upload the picture twice. I tried to upload a video showing that the sprocket is loose. The plate holds it in place so it won’t come off, but there is a lot of side to side play in the sprocket itself.

remove the bolts , then the plate can move separately from the sprocket.
The plate is sitting in a groove rotate it and slide it off the spline. Then slide the sprocket off.
The Sprocket will be a bit loose but from what i have read here it seems to be normal and isnt a problem

Manual & Sprocket. What manual are you using? There's a Kawasaki FSM pdf available for your bike.
Pg 225 shows a Z250 Fr sprocket that appears to have the same setup as yours with the same output shaft & sprocket holding plate.
A number of models have the same method of securing the Fr sprocket. seems like it would float around on the output shaft. which is rather strange to me. I would be sure to check & adjust the drive chain correctly & don't let it get loose, and if worn/stretched, replace it.

ps: Is that sprocket worn or am I wrong? I compared it to new sprockets on eebbaayy, but I'm not sure. part # 13144-1046

That sprocket needs replacing and Im guessing the chain and rear are equally as bad judging by the wear on the front.

This is a good time to remind folks that the chain and sprockets should be replaced as a set: putting a new chain on worn sprockets will cause accelerated chain wear, and an old chain on new sprockets will accelerate sprocket wear..

I changed the gearing on one of my bikes and did the whole set, even though the only change was the front sprocket and everything was still serviceable. Now I have a set to re-install if I ever want to go back to the stock gearing.