I have a Steam Key for a different BloodRayne game that you can have, it's the first link, not the second link.
They're the same game, but it got a remaster, you can't buy the older version on Steam anymore, but it has lower System Requirements (good for your potato!)
The purchase option on the "Legacy" page shows that you're actually buying the "Fresh Bites" (new) version, I'm not sure if that also gives you the Legacy Version, but whatever, that's the only one I can give you for free.
Do you want it?
The original video game femme fatale, Rayne, has returned to battle and feed in a brand new hack ‘n slash adventure. Slay ghastly enemies as Rayne, the sexy dhampir with superhuman strength, speed, and agility, recruited by the vampire hunting Brimstone Society for one last mission.
store.steampowered.com
Original developer WayForward upgrades its 2011 classic with new voice acting by Laura Bailey and Troy Baker, sharpened visuals, and rebalanced gameplay. Run, jump, cut, and feed your way through a massive underground castle to confront Rayne’s father at the behest of the Brimstone Society.
store.steampowered.com