If you mean what ODM they use, hard to say. They used Quanta for the last one, same as a lot of PC companies, but that was also when you could more easily manufacture in China. Dropping the screen also means manufacturing is a lot easier, panels are the hardest component to move out of Asia.
The Steam Machine would be cheaper if it used the same components, but it's shipping with much larger silicon and more storage and memory. The last two are very expensive right now.
You're claiming that Valve could offer a $100 subsidy per unit. That means they need to sell $300 in games in order for their 30% cut to pay for that subsidy. Hence I don't think it's realistic to expect every person who buys a Steam Machine to spend $300 on games they would have otherwise not bought.
You're treating this scenario as if 100% of revenue from each game purchase goes to Valve, when in reality it's a max of 30%.
We'll see. Xbox is going into a completely different price range next generation it sounds like. So it's really only PS6 maybe in that p[rice range, gaming desktops don't really compete in the $600 to $700 price range in any meaningful volume.