Think about it. He’s able to take control of Eagleland easily save for a couple children who actively resist. He has immense power, similar to that of which Ness, Paula, and Poo have. Old ones typically have incomprehensible forms, and when Giygas appears in the final fight, you only see the background. To add to that most of his attacks are simply unknown attacks, which have various effects.

Plus the way you beat him, story wise, is through Paula’s prayer. Which is basically defeating him by having people praying for the 4 characters to be safe, which could be taking power away from Giygas before his defeat.

This is just a theory but I kinda like it. Also I haven’t played Earthbound Beginnings but I know he’s an alien in that game, but it could just be a taken form for the sake of comprehension, like angels appearing as humans with wings.