The Game Audio Tutorial is indeed a great resource, but its biggest advantage is its biggest disadvantage: it really is UDK-focused.
That's OK because UDK is a complete, important and really good tool, but it has its own audio system, unrelated to anything and clearly less a priority for Epic than almost all graphic features.
Note that the tutorial level detailed in the book is freely available for anyone, if you just want to have a look at it.
If you want to get a good grip on a complete game engine anyway I think you should rather look for:
- Unity which is easier to learn, use, has a huge user base and documentation available everywhere
- or the CryEngine 3 which rely for its audio part on Fmod, one of the "standard" audio tool in game industry (see below)
All of the precited tools are free to try anyway.
Or, as stated above by Stephen Saldanha, you can try one of the game engine-agnostic audio tool, Fmod or Wwise. Both of them are currently in use for a lot of AAA titles and for a few indie ones.
They're made of an UI part - a simplified DAW where you associate sounds with "events" to trig in-game (for instance a creaking sound when opening a door, etc.) - and a code part which allows you to call created events when things happens in your game. Integration into some game engine like CE3 allows to do all of that without having to write a single line of code.
- Fmod is the "programmer-oriented" one, with a really nice programming interface (which makes it easy to integrate in game or learn how to program audio software) and a simple UI.
- Wwise is the "sound designer-oriented" one, with a nice (although messy) UI and - that's my opinion - a terrible programming interface.
Both are them might be described as "easy to understand, hard to master"; these are huge machinery entirely dedicated to audio, which will prevent you from being distracted by anything else (as it might be the case with UDK, CE3 etc.) but will have to be integrated into a game if you want to create a working prototype.
I am more on the audio programmer side but I have worked with all these tools, both on the sound design and programming/game integration parts. I know a few complete beginners, non-programmer which have tried all of these tools too...and, well:
- I think that Unity is the definitive great choice for beginners; the audio part is a bit less sophisticated than the others but getting started on it is no more than a few hours work.
- If you really think you can discipline yourself enough for it, you could try the CE3 + Fmod combo; I think that these are the most powerful and modern tools - but that does not means at all the best nor the most widely used.
Good luck anyway, and do not hesitate to ask if you have any further questions !