Doing more testing by editing the configuration file to add the input configuration, I found something additional in the log file:
Input: 0 SDL joysticks were found.
Input: N64 Controller #1: Forcing default keyboard configuration
Input Error: Couldn't find config file 'InputAutoCfg.ini'
Input Warning: missing 'plugged' parameter from config section AutoConfig0. Setting to 1 (true).
Input Warning: missing 'plugin' parameter from config section AutoConfig0. Setting to 1 (none).
Input Warning: missing config key 'DPad R' for controller 1 button 0
Input Warning: missing config key 'DPad L' for controller 1 button 1
Could it be that in Emulstation the Picade is seen as a keyboard but in the "game" as a joypad? This could explain why the inputs are not matching anymore, no?