To many individuals' dismay, playing your games in full screen can be a pain, especially if your character's movement is continuous and controlled by the position of your cursor.
Each browser seems to have its own variant of this issue. Some show a dropdown X while others drop their address and title bars. In each case, you lose control of your game or character during the dropdown phase. In many browser based games this makes moving "up" more challenging as you have to keep the cursor away from the top of your screen.
That being said, there isn't any HTML that can prevent this and in the case of Chrome, for security reasons Chrome extensions lack the ability to directly communicate with the operating system's API.
For Windows users specifically, this can be done using the ClipCursor API.
I have recently written and released a tool for Windows called Browser Cursor Lock that does just this. Its written in Autoit, is free to use and also open source.
Have fun playing!