There are two different versions of SharePoint. There is the On-Site SharePoint and Office365 SharePoint. The process can be a little different in terms of getting the Camtasia produced files to play on SharePoint. Below are a couple videos showing how to get the files onto your SharePoint in both scenarios and also how to configure SharePoint so it plays the video back properly.
Uploading Camtasia Files to SharePoint
Configuring Office365 SharePoint to Play Video
Configuring On-Site SharePoint to Play Video
Go to Central Administration > Manage Web Applications > [Highlight a web application] > click General Settings in the Ribbon > Scroll down in the General Settings window to see Browser File Handling. Set as Permissive. Save settings. Now when you click to play the HTML file it will play the video instead of prompting to download the file.
Known Issue with iOS 10
There is currently a known issue introduced with iOS 10 that will prevent mp4 video files from loading. In iOS 10, the html5 video player is not sending authentication cookies to the server, which are required to load the mp4 video file. Please see this Apple discussion for more details.