That's another area where TWO is ahead of WGT. TWO offers a dedicated keyboard shortcut for switching to full-screen: the F2 key. TWO also offers dozens of other extremely useful keyboard shortcuts.
In contrast, there is a single dedicated keyboard shortcut in WGT: pressing the SPACEBAR for switching to Zoom view & back. That's too bad, considering all the untapped potential of keyboard shortcuts.
So in order to switch to full-screen in WGT, you need to use your browser's keyboard shortcut, rather than a game-dedicated shortcut. In most browsers, it should be enough for you to press the F11 key to switch to full-screen. However, I've found that this is buggy in WGT; it sometimes works, sometimes not.
In order for it to work always, WojciechMigda advised us the trick of launching the game from the direct link, rather than from the pop-up window. Just bookmark this link and click on it:
http://www.wgt.com/gameclient.aspx
A full-fledged browser window will open, with the Menu items and commands intact. So, just go to the (for example) View => Full screen menu in your browser to play this golf game in full screen. This works every time.