Well there are series in which you'll def miss out if you haven't played any of the games, the only case that would count for me is Devil May Cry, though the anime isn't literally one of the games but then animated. If you start playing DMC then you'll get how great it actually is because you do things and don't just watch
As for Basara, the game if I recall correctly was more of a streetfighter game so you wouldn't miss out much in those cases it would be anime before game IMO
It all depends on what kind of game it is in the end
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