Yes, it is unprofessional to leave without the standard 2 weeks notice but, as has been pointed out, you aren't far into the project and these are special circumstances.
If it were me, I'd confront the boss directly. Lay out, as unemotionally as possible, the incidents that cause problems. Try to use "I" language as much as possible. It may not make any changes in the boss but it's good practice. This isn't the first time you may run into this situation and the more practice you have dealing with personality issues the more successful you will be in your career.
If the boss is as impossible as you have described him (and I've met more than one that were pretty bad) he won't receive the talk well. At the point when it becomes certain that you are getting nowhere, you can tell him you've made the decision to leave the company, and this is his one week notice or however much you've decided to give him.
It is just barely possible that he is completely unaware of his behavior and will be open to making changes and then you have a more difficult situation. You may still decide to leave, but then at least you have left him with something helpful and not burned any bridges. You may think that it doesn't matter, you'll never see this guy again but you never know. People are very mobile, and they talk. Always conduct yourself with as much professionalism as possible.
If you are very uncomfortable with a face-to-face meeting, send him an email. As above, start with a frank discussion of what you are having problems with and give him the chance to respond. If you run into problems you will have a paper trail to cc his boss in on, should that become necessary.
If you are afraid of giving yourself a black mark with your new company, don't be. If they are a good company to work for they will be looking for someone who is both professional and loyal. You demonstrate both qualities by explaining that you need to give at least some notice. Tell them that your current company may not require you to work for the full time period because you had been with them such a short time, and leave yourself the option of maybe starting the new position right away if your boss gets POed and fires you.
As for not wanting to spend any more time in an unpleasant situation than you have to, I can certainly understand it. However, the fact that you know "it's only for another week" may make it easier, and once you start choosing the easy path over the professional one it makes more slippage likely in the future. For your own sake set your standards as high as you'd like to see in your coworkers. If you were a boss and one of your employees had a problem with you how would you like them to act?