Cats make a variety of noises that people call different things. I'm not sure they're generally one thing or another, and lots of people have categorized them into many different types. Because science! Here's my speculation, though:
Okay, okay, all jokes aside - I'd call that noise a chirr or trill. Wikipedia has a great amount of information on cat communication, condensed for easy understanding.
Schötz categorised vocalizations according to three mouth actions:
sounds produced with the mouth closed (murmurs), including the purr, the trill and the chirrup,
sounds produced with the mouth open and gradually closing, comprising a large variety of meows with similar vowel patterns, and
sounds produced with the mouth held tensely open in the same position, often uttered in aggressive situations (growls, yowls, snarls, hisses, spits and shrieks).
I reason it’s a chirr because it’s more intense than a regular purr. (Fun fact: no one really knows how a cat purrs!) It’s a friendly, greeting-type noise, so you should be happy your cat communicates with you like that! I know mine often does when I talk to her. She responds in chirrs. The Wikipedia page linked above says this about chirrs:
The chirr or chirrup sounds like a meow rolled on the tongue. It is commonly used by mother cats calling their kittens inside the nest. Kittens recognize their own mother's chirp, and do not respond to the chirps of other mothers. It is also used by friendly cats when eliciting the approach of another cat or a human. Humans can mimic the sound to reassure and greet pet cats.
My kitty talks to me like this all the time, in "response" to my questions. I'm happy to know it's a friendly noise!