I assume you are producing out of Camtasia using the TechSmith Smart Player production path. If you are hosting the TechSmith Smart Player you will not see a full screen button if the following are true.
The web browser does not support standard web full screen api. Right now that is true for the Safari browser on the iPhone within the browsers we support.
You are hosting your Camtasia produced HTML in an iFrame that does not contain the "allowfullscreen" attribute.