You're right, it doesn't make sense that the .EXE file fails to run (duh). Here are the file sizes that I have, and definitely worked for me:

setup_baldurs_gate_2.exe - 2.34 MB (2,456,790 bytes)
setup_baldurs_gate_2-1.bin - 1.95 GB (2,097,542,912 bytes)
setup_baldurs_gate_2-2.bin - 325 MB (341,565,909 bytes)

I just downloaded all three files and then installed the game - everything's sorted now.

I experience the same issue.

I downloaded the game via the downloader, and it finished with:

baldurs_gate_2_complete_part0.gogDownload
setup_baldurs_gate_2-1.bin
setup_baldurs_gate_2-2.bin

No executable whatever. Seperately downloading the installer .exe and placing it in that directory only made it vanish (!) upon execution.

I'm now downloading the game via regular download (funny enough, with twice the speed of the Downloader).

*Edit: Adding the .exe and deleting the .gogDownload file solved the problem. Annoying issue nonetheless.