Origin installs, just like Steam, an own protocol which you can use to run games.
This would launch the game "Wing Commander 3" if you have it installed. Unlike Steam, it would not bring up the installation dialogue, if it is not installed. To find out the product id, you would need to dig into the website code for each store page. I am not sure if this product id is the same for all countries like on Steam, but even there different AppID's for the same game do exist, such as low violence versions etc.
If you do not own the game you try to launch, you get a Window that tells you to activate the game via a product key.
Simply running origin:// launches Origin on the computer.
Example from the German Wing Commander 3 Page:
The highlighted ID is the one you are looking for. The store appends
to the URL as it would indicate that this can be used to download the game. But my tests with this have been unsuccessful so far.
It is a bit of a hassle to find the correct product code. Especially for games like Sim City, my tests have been unsuccessful. But in theory, you can use this to control your games without touching Origin. However, Origin comes to the front if you run any of these commands.