So CPU usage is independent from bitrate. Lowering or increasing bitrate (within reason) doesn't affect CPU usage. The encoding presets, the image size and framerate, and the video complexity are the biggest ways that CPU usage is affected one way or another.
Eurotruck:
19:38:27.658: [x264 encoder: 'simple_h264_stream'] preset: veryfast
22:06:57.103: Output 'simple_stream': Total encoded frames: 267283
22:06:57.103: Output 'simple_stream': Total drawn frames: 267283
22:06:57.103: Output 'simple_stream': Number of skipped frames due to encoding lag: 1129 (0.4%)
22:06:57.103: Output 'simple_stream': Number of lagged frames due to rendering lag/stalls: 92 (0.0%)
Looks good.
DayZ:
22:39:22.225: [x264 encoder: 'simple_h264_stream'] preset: ultrafast
22:45:21.380: Output 'simple_stream': Total encoded frames: 10774
22:45:21.380: Output 'simple_stream': Total drawn frames: 10774
22:45:21.380: Output 'simple_stream': Number of skipped frames due to encoding lag: 231 (2.1%)
22:45:21.380: Output 'simple_stream': Number of lagged frames due to rendering lag/stalls: 7 (0.1%)
Not good. 2.1% skipped due to encoder lag is too many, my rule of thumb is this needs to be under 1% to look decent when the video is watched or played back.
H1Z1:
22:47:12.929: [x264 encoder: 'simple_h264_stream'] preset: ultrafast
The H1Z1 log file is incomplete and the encoding statistics aren't present. Did you copy the entire file or miss the end of it?
So anyways, it looks to me like DayZ has a far higher visual complexity than Eurotruck, meaning its simply harder to encode. Too much for your computer's CPU. You could try to lower your streaming resolution as Fenrir suggested, and I'd add a suggestion to leave your bitrate the same as if you were streaming a higher res, which will help things a bit.
A forum search seems to back this up:
https://obsproject.com/forum/search/10046730/?q=dayz+grass&o=date
Downscale the stream, not the game. I'd go with 480p30. Play it with lots of that nasty grass on the screen in high action situations for at least 5 minutes, then look at the log files. If you're getting skipped frames due to encoding lag over 1%, go smaller. If not, go with what you have or test a better preset.
And btw, Eurotruck looks fine, you need different settings for the two games.