I don't see what issued one would face with "This Game", though? I personally thought it was a fantastic opening and Konomi Suzuki cemented her place as one of my fave artists with that song (and a few other works I've listened to in the past - Watamote and Freezing S2 openings, namely).
As for NGNL, well, this is what I think (heh, another tl;dr incoming!)
Firstly, the thing that impressed me the most about the show were the aesthetics. I LOVED how everything was so freakin' colorful. It probably turned some people off due to the so called "over-saturation" but I think they struck a good balance between saturating the screen with all sorts of colors and making it extremely obnoxious. Also liked how the real world looked relatively monotonous with those B&W colors. That, and I thought that the animation was pretty well-handled. The effects (DEM EYES) were particularly stylish. :3
There was nothing that stood out a lot from the OST - nothing particularly remarkable but I thought it was fitting for the most part. Nothing felt incredibly misplaced, at least.
I do agree that some of the games, the chess one especially, didn't make any semblance of sense. But then again, NGNL is one of those series where the perspective you choose to go with - going into the series - plays a large role in determining the amount of enjoyment you'd get out of the show. After the game of cards (first episode), I stopped thinking of it as an anime that'd concentrate on things making sense and on genuinely intellectual tricks but would rather focus on being a "fun fun cool shit fun fun" anime. As a result, underwhelming as the chess match was, it still didn't make me feel all salty/bitter about the anime. In fact, as a result of my attitude towards the show, I greatly enjoyed the game they later had with Jibril. Naah, not just that (although it was THE peak the show attained as far as my opinion goes), I greatly enjoyed everything the show threw at us that point onwards.
Sora and Shiro were both fairly lacking in depth. But I usually don't look for depth in shows like NGNL, you know, ones that serve no other purpose than to entertain you on a weekly basis, so I was fine with that. Other characters were just there to compliment them and serve as set-pieces of sorts. They served no other purpose than to make Sora and Shiro look cool doing cool shit. Which they succeeded with, I guess, judging by the amount of fun I had with the series. One character that could've been handled better was the red haired female human character. But that's just one issues I have with the series that didn't detract much from the fun I had with it, overall.
One thing that seperated this series from stuff like SAO, I think, is the fact that it doesn't seem to take itself as seriously as the others. It knows it is spouting shit that's supposed to sound cool - it does that in a totally flashy way and isn't weighed down by annoyances like unnecessary drama and serious sub-plots. Inclusion of those elements probably would've made it worse since none of the characters were interesting enough for me to actually be interested in character-drama involving them. Hence, the approach that it took (concentrate on DA COOL SHIT, YO) worked for me.