The emulator code is open source. However, ROMs are copyrighted . The MAME 2003 Plus archive contains data dumped from arcade cabinets. Legally, you should only download ROMs for games you physically own the original arcade PCB for.
Using the Mame 2003 Plus Roms Archive is relatively straightforward: Mame 2003 Plus Roms Archive
Because of the popularity of the Raspberry Pi, curated "MAME 2003 Plus Reference" sets circulate on archive.org (a legitimate digital library). You are looking for collections labeled: The emulator code is open source
(from 2003), it includes fixes and support for hundreds of additional games backported from much newer versions of MAME (up to 0.188). Performance Optimization: Mame 2003 Plus Roms Archive