startx will just start the X server / environment and by default just start xterm, not the browser (You also shouldn’t be running it as root). RetroPie doesn’t come with a full X desktop environment to keep the size down.
if you have installed midori, you can start it by installing a window manager and making a small script
sudo apt-get install matchbox-window-manager
then create a script in your homedir called browser.sh containing
#!/bin/bash
matchbox-window-manager &
midori
make sure it has executable permissions (chmod u+x browser.sh)
then you can do
xinit ~/browser.sh
to launch X and run the script which loads the window manager and browser.
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