I was in the stadium and Klose's movement (that's the thing that you don't see on the TV and can't always find out based purely on statistics) was fantastic. He knew exactly how he could break the defence. The only thing I disliked was his first touch, he lost quite a few balls because of that in the first half. It got better in the 2nd half though. It wasn't surprising btw to see Özil performing that great, the guy loves playing with Klose.
Özil improved because there was in general more moving upfront. Khedira was almost always upfront (4-1-4-1) and Schürrle and Reus provided much more intensity to the German game. Also and that's a point, it was much colder (~20°) than the games before. The fact that all these players did run more has _nada_ to do with the player upfront. Klose had an average match (which isn't a bad match how some in here try to ascribe to the more critical users of his performance) and I would also rate the contribution of Gomez in the match against Denmark superior to Klose's against Greek. In detail Gomez did all the things that are "usually" denied by others. He's gone wide, created space, nice first touch, nice overview and Poldi scored. Nontheless it was a nice tactical move to start with those three new guys. It makes the team unpredictable which is a huge benefit.
You can take the Greece game completely out of the equation if you want but the fact is that the difference Klose makes and the impact he has has been evident for years with the team. Look at the Brazil game last year for example.
Klose had a brilliant match , and just missed several assists , btw. He reads situations so well, and the key thing that he knows how to do that Gomez doesn't is when to get the hell out of the way. Go back and look at the sitter that Oezil missed. Classic Miro reading the situation, and knowing how to move the centerback out of position. He's not fully sharp yet, but his mental quality allows him to contribute. When Gomez isn't poaching, you get nothing from him offensively. These new apps are giving kids the impression that you break down player performance with heat maps and distance covered. This is not how you evaluate players. You analyze situations throughout a match.
The stats are really great but if you don't know how to read or use them then they're pretty pointless.
You noticed that in the last 10mins when Gomez came in, He assisted Ozil for 2 moved which he failed to take which he did exactly what you said Klose did "Taking the CB out of the way".