As you suggested, I ticked the "Use file name only..."
However, the other problem I was having was with the naming of the roms, or so I believe. Although the roms were showing up on Launchbox, some of them were not running. I simplified the names, removing all spaces and strange characters and that made them work. I believe Mame has some problems with weird named roms. Another strange behaviour inside Launchbox, was that after importing the roms and selecting the option to leave the roms in the original directory, the rom folder listed in the details of the Platform was something like "Games\Sinclair ZX Spectrum"...so I redirected it to where I had imported the roms from originally.
By the way, the reason for running these platforms through MAME is that I can get the amazing look through the HLSL shaders and the ease of customization. I just love the phosphorous trails and never found anything similar in other emulators. It really ends up looking the way I remember...