I am having the same problem on my Gentoo system (running openJDK 11.0.3_p7-r2). I have tried both the .tar.gz and .deb package with the same result. However, the same launcher runs fine when installed on Ubuntu 16.04 LTS. Here is ldd output from my Gentoo system:
linux-vdso.so.1 (0x00007ffc5e3c3000)
libdl.so.2 => /lib64/libdl.so.2 (0x00007fe63b350000)
libpthread.so.0 => /lib64/libpthread.so.0 (0x00007fe63b328000)
libstdc+.so.6 => /usr/lib/gcc/x86_64-pc-linux-gnu/8.3.0/libstdc+.so.6 (0x00007fe63b120000)
libgcc_s.so.1 => /usr/lib/gcc/x86_64-pc-linux-gnu/8.3.0/libgcc_s.so.1 (0x00007fe63b100000)
libc.so.6 => /lib64/libc.so.6 (0x00007fe63af30000)
/lib64/ld-linux-x86-64.so.2 (0x00007fe63b380000)
libm.so.6 => /lib64/libm.so.6 (0x00007fe63ade0000)
Galen, thank you for pointing me to ~/.minecraft/launcher_log.txt! Once I looked there, I found a log message indicating that I was missing gconf, and once I installed that, the launcher started.