Okay. Just putting this here while I’m on lunch break. Basically putting in comments to say what each step does. Try running each of them individually, and report back on what the output is, if any present an error. We can work it out from there.
#DOWNLOAD AND INSTALLATION OF DEPENDENCIES AND BINARY
wget -O /home/cpi/mupen.sh https://www.dropbox.com/s/uxerntgv8kpluzm/mupen.sh?dl=1 && chmod +x /home/cpi/mupen.sh && ./mupen.sh
#CLEANUP OF INSTALLATION FILES
sudo rm /home/cpi/mupen.sh
sudo rm -r /home/cpi/mupen/
#OVERWRITE EXISTING MENU ITEM
wget -O -rf /home/cpi/apps/Menu/20_Retro\ Games/mupen64plus/action.config https://www.dropbox.com/s/932qp0yqjeta8ot/action.config?dl=1
#MAKE CONFIG DIRECTORY AND INSTALL OPTIMAL CONFIGURATION
mkdir /home/cpi/.config/mupen64plus/ && wget -O -rf /home/cpi/.config/mupen64plus/mupen64plus.cfg https://www.dropbox.com/s/9msh8d8js2tek9k/mupen64plus.cfg?dl=1
Wait. Did you copy each line, one at a time into your SSH session window, or just copy the whole lot, and pasted it in? That could be the problem, if at any stage one off the steps halted.