Not an answer, but some more info: It looks like files for benchmarks are in the game folder: conf/benchmark has a few "cfg" files. They point to missions which are listed in the packs/00_win_data.zip missions/benchmarks folder. I have version 1.33 installed currently.

So the mystery is how to load those benchmark configs, and whether the GOG build is compatible with them (some of the cfg files have "steam" in the name). I'm not sure if the configs have to change in "Documents\The Riftbreaker" folders. There's a Documents\The Riftbreaker\config\local.cfg which has a syntax similar to the benchmark_intense.cfg from the game folder, but I don't know if copying options from one of the benchmark configs into your local config would have the desired result. There could be flags which have to be added to the Launch shortcut, I don't know.

If someone has the GOG demo installed, it'd be good to know whether it has an option to run the benchmarks; that could be another option, although not quite as useful as benchmarking the current build.

The devs made a post which sounds like they run nightly benchmarks against new builds (to make sure it handles intense scenarios properly, etc.) so I'm sure the functionality hasn't been removed from the full game entirely, at least the devs still use it internally. Hopefully it's not just in their development builds. You could also try to ask them on their "official Discord server" which is in the game's main menu.

Just FYI, there is a workaround for now but it's not great IMHO.

1) Go to the install directory [install path]\The Riftbreaker\conf
2) rename the inital_config.cfg to something like _initial_config.cfg
3) copy one of the benchmarks in the conf\benchmark\ directory (like benchmark_gpu.cfg) to the conf directory
4) rename that file to initial_config.cfg
5) run the game and it will play the benchmark.

Things to note, the benchmark just ends and goes back to the desktop. You have to tweak the cfg files manually with a text editor. I didn't run it from the launcher so I don't know if running it that way will edit the cfg file.

To get back to running the game just rename the initial_config.cfg to something like BenchGPU_initial_confg.cfg then rename the _initial_config.cfg file back to initial_config.cfg and run the game again to play normally.

I am certain there has to be a way to specify what cfg file via the command prompt but I don't know what it is. I tried:
riftbreaker_win_release.exe [install path]\conf\benchmark\benchmark_gpu.cfg
riftbreaker_win_release.exe -config [install_path]\conf\benchmark_gpu.cfg
... -c ...
and none of them ran the benchmark. So the only option at the moment is the above unless one of the devs would like to tell us what command line parameters we can pass to the exe file to specify the config file we want to load.

I am not marking this as the solution because IMO it is just a partial workaround. The solution should really be something like a command line parameter we can pass to specify the config file we want to load.

Pretty old but this is the first hit in google so here goes.

The secret sauce is "config=foo\bar\config.cfg" that you need to append to the command line. So, for example, this:
riftbreaker_winstore_release.exe config=conf\benchmark\benchmark_intense_dx12_tc.cf

Note that the benchmarks do not pick up your settings so you have to go get the "local.cfg" from "%UserProfile%\Documents\The Riftbreaker\config"
and do some cut + paste to tweak the settings to taste. I'd recommend backing up the original benchmark file 1st if you make a mistake..

Unfortunately, the release version doesn't do any kind of report screen, so you have to eyeball how it runs with fps display, but c'mon, isn't that enough?