Yep, territorial is the right word, they feel the space is theirs and they see it as a menace so they defend their territory with everything they have. That is why I feel that jealous is not the right word, it's a territorial matter.
I love kittens but cats not so much LOL I find they get very jealous, territorial and very possessive of their owners. I have never owned a cat in my adult life, but I grew up around them and boy, they can be mean LOL I also don't like their ice-cold, stand-offish attitude. I can see them being very unwelcoming of new cats in what they deem as their space.
My issue with cats is that I am allergic to them, so I can't be around. Also, I always was a dog person because I find them more friendly. My parents did have a cat and it was a huge passion they had.