This is a slippery slope because there's tons of example that are hard to define even outside of video games example. There's some anime season that are completely different from their manga counterpart. Dragon Ball Super for example is either original or an adaptation if we have to make a difference between following the original plot or not. Most anime movies would also be. Should the Naruto filler seasons be considered original?

And if they are loosely adapting, where would be the line between original and adaptation? 4-koma anime adaptation usually take the gag but rewrite them into some loose plot, is it still an adaptation or an original? God Eater anime adapt the universe yet change the plot completely compared to the game while keeping the overall structur, adaptation or original?

The only defining factor for Original production when I was working in the anime industry was wether it was based on an existing IP or if it was a new IP. It's a simple definition with a clear cut answer (except for some crossmedia projects but those are still usually considered original unless the anime was not plan for the initial release plan of the project).