I believe it's just one of those words which has been adapted from English. If you go to Wales you see signs saying things like 'dim smokio' (no smoking), 'dim parcio' (no parking) and 'dim entrio' (no entry). I think the nature of the Welsh language is such that most recent additions have come from English.
Most places say "dim ysmygu" for no smoking though you might hear people use smocio in conversation, and "dim mynediad/mynedfa" for no entry. I'm a native speaker and entrio is definitely not a word, not even a borrowed word from English. Parcio is correct though. A car park is called a "maes parcio".