Yes, if you wish to sync desktop Windows sticky notes with Notezilla.Net cloud then you will need to install Notezilla Windows version on each system. Notezilla.Net web app can be accessed from any Internet Browser on any device. So there is nothing to install if you are going to use the web app.
We have launched Android, iPhone/iPad apps recently. You can use them to download & enable automatic sync of all your notes every minute. More details over here: http//:www.conceptworld.com/Notezilla/Notezilla.Net