The runcommand dialog prompt which you get is actually present since the game start, it's just obscured by the emulator that starts and overlays on-top of it. The dialog being present after the game ends means that the emulator hasn't actually exited/stopped - in order for EmulationStation to pick-up and start - and it's stuck somewhere.

This may be a sdcard issue - emulator tries flush some state to the disk on stopping the game or saving the options file and not being able to will block the emulator. Your log file is strangely formatted (did you copy/pasted from a SSH session or OCR-ed a photo ?), but it doesn't show the emulator actully stopping, which would show something like:

.... ^C[INFO] [Core]: Content ran for a total of: 00 hours, 00 minutes, 04 seconds. [INFO] [Core]: Unloading game.. [INFO] [PulseAudio]: Pausing. [INFO] [Core]: Unloading core symbols.. [INFO] [Core]: Saved core options file to "/opt/retropie/configs/all/retroarch-core-options.cfg". [INFO] Threaded video stats: Frames pushed: 244, Frames dropped: 0.

If you have SSH available, you can the emulator through strace and the post the strace log archived somewhere (it's going to be too large to post the contents as is), just to see where it's stuck. Stop EmulationStation and run:

strace -f -o strace.log /opt/retropie/emulators/retroarch/bin/retroarch -L /opt/retropie/libretrocores/lr-fbneo/fbneo_libretro.so --config /opt/retropie/configs/arcade/retroarch.cfg "/home/pi/RetroPie/roms/arcade/frogger.zip"

then exit the game. When it gets stuck, then save the strace.log file and upload it somewhere.

EDIT: strace is not installed by default on RetroPie, but you can install it by running sudo apt -y install strace. I also advise to update RetroPie in order to get the latest version of RetroArch and OS packages available.

Runcommand not showing before rom load.