It's not just the Game mode. I didn't even bother measuring the Game mode but it's easy to see the problem form Cinema mode results: even the SDR range (0-120 nit) is heavily dimmed on my 55C7 (EU v04.70.10) if the metadata indicates 10000 nit peak white for the source.
The only HDR capable game I own right now is ME:Andromeda. This definitely uses 10k metadata (one can validate that by fiddling around with the developer console and the built-in "display calibration" GUI: the game displays a peak white and an adjustable gray box in the settings menu, where the adjustable box can be set in plain number to a desired brightness in raw [nit] from the developer console).
So... yeah, LG is trying to be "way too smart" and they seem to think their customers are even more stupid. They seem to think it's more important to preserve the geometry details in blindingly vibrant portions of images rather than providing standard brightness in the usual low-light portions. They are sacrificing the "correctness" on 99% of the content to make 1% "somewhat better". And then they say customers should just turn on Dynamic contrast which might look better at first but it isn't really just what you might think it is.
Even the Low setting (dyn.cont.) throws color accuracy out on the window (and higher settings make a mess out of overall color acc.) and you would actually need High to compensate for the heavy dimming. Hell, even High isn't enough to bring 10000nit input back to correct SDR brightness in the SDR rage (don't let yourself to be fooled, just because it might look "good enough" at first, it doesn't mean it's all great). Dynamic contrast adjusts the brightness of different colors (grays or saturated primaries for example) differently, so the resulting color space is very non-standard.
It's bothering enough for movies mastered at 4000nit. Genuinely dark scenes are notably darken than they should be (even if it's far from being as bad as it is with 10000nit metadata with games, it's noticeable with 4000nit movies too!) The small difference with 1000nit movies is pretty much impossible to tell by the naked eye (may be if you have a reference screen side-by-side, or not even then).
I's easy to see the error created by Dynamic Contrast by the naked eye: pause a 4000nit masteres movie at a dark scene which contains some saturated colors and white. I used a scene form Fantastic Beasts where I could see a flag (red, white and some other color bars I can't recall) in a dimly lit room at night. If you start cranking up Dyn.C from Off to High, you will notice that the white bar in the flag rises in brightness a lot faster than the saturated color bars. In other words, the white bar in the flag started to look like a dim neon light was installed behind it (while the colored bars looked pretty much the same, even if a little brighter).
Well, games can look better or worse subjectively depending on the actual game and specific scene.
MEA was a true "laser show". It almost hurt my eyes when I tried to aim at the bright red lights in the almost pitch-back underground facilities in HDR mode. (But that's by design, it was the game's "fault" and I could always just lower the peak brightness either from the game settings or using the OLED Light and/or Contrast settings of the TV, or both of these, I could make it as dark as I could possibly want...) So, yeah, it's almost better at first when it's dimmed (like now). Although, if I go outside (I mean still inside the game's world...), I find the sunny desert disappointing. It should be stunning (almost blindingly bright as you would expect from a desert) but looking at the sand on the ground gives me the feeling of a cloudy day (just with the actual clouds missing from the sky, like it's a graphic glitch in the game).
In my opinion the SDR range should never be compressed (no matter what) and even the 120-650 range (rough peak on these displays) should offer a choice for plain "hard clip" rather than "roll off" via a user switch (but I wouldn't really miss that if the 0-120 wasn't messed with).
I could try compensating for this with a 3DLUT but it's complicated if the ABL is involved (and it easily will be in HDR).