From the log, it is clear that groovymame is not able to switch to native game resolution based on its calculation. It runs using the X default resolution instead.
SwitchRes: v0.015l, Monitor: custom, Orientation: horizontal, Modeline generation: enabled
SwitchRes: Monitor range 15625.00-16200.00,55.10-65.00,2.000,5.700,8.000,0.064,0.192,1.024,0,0,192,240,0,0
SwitchRes: Monitor range 15625.00-16200.00,49.50-54.25,2.000,5.700,8.000,0.064,0.192,1.024,0,0,192,256,0,0
SwitchRes: Monitor range 15625.00-16200.00,49.50-65.00,2.000,5.700,8.000,0.064,0.192,1.024,0,0,0,0,448,576
SwitchRes: Found output connector 'VGA-0'
SwitchRes: Entering switchres_modeline_setup
SwitchRes: v0.015l:[cninja] Calculating best video mode for 256x240@58.000000 orientation: normal
SwitchRes: ( 1)x( 1)_(60=0.0000Hz) - locked
SwitchRes: could not find a video mode that meets your specs