So basically for $9.99 I just buy half life 2, and then I have a complete access to royalty free use that engine to build a game?
No.
You can actually get it for free (without even buying HL2)... but that doesn't give you a license to do what you want with it.
You can't sell your creations without negotiating (buying) a license from Valve.
If you want to make a free game/mod, or a freely available prototype of a game, then it may be suitable for you.
The engine is not something for cutting your teeth with. It is something a professional studio with an experienced teem of veterans in all disciplines could leverage.
I cut my teeth on GoldSource (though Unity/UDK didn't exist at the time), and would recommend the same path to others who want to learn C++ game programming. Sure it's complicated, but you'll gain a lot of exposure to and experience with real-world, shipping C++ game code, and real-world, non-user-friendly tools and pipelines