The kingdom of Argus is where it all starts obviously. According to the PS2 manual, Rygar is an expert swordsman with no memory of his childhood. Without spoiling this game for you, it is clear Rygar prevails at the end and lives to fight another day. This leads me to believe that Rygar travelled to Argool to fight Liger (The arcade version) and of course was victorious. After this, Rygar dies. How he died is unknown.
Decades (or centuries who knows..) later, he is resurrected from the dead to battle Ligar once again in his floating castle above Argool (NES version) at the end of the NES game it says
"The warrior who finished his fight returned to Argus"
Does this sound plausible as the story of the whole series?