"Alive" in that context was clearly referring to "being with emotions/feelings/consciousness". The robot that was in the scene, by virtue of being a robot/AI, should solely be a mere being following lines of codes, and it's true, this is what is explained in the verse, but that still means it has some sort of Ego.
Unagami is similar. It's a being made wholly of data, but it has a consciousness, even if that being is only in the game instead of roaming the Real World.
All the characters here are "real", 100%, but some are virtual beings (10-C) while others are "real beings" (whatever tier you want them to be).
The moment a monster or character from the game world gets into the "real world" they stop simply being code within a video game but instead become "real" or, well, at least not limited to the virtual world anymore, hence why they retain their abilities, power etc.