No in-universe explanation, but...
1) Assuming the first models of Terminators (like the drones from T3: Rise of the Machines) were built/designed - not to mention repaired - by humans (rather than by robots and computers), it would make sense to put some sensor- and debug-information on the video/data-stream. When so the robots started building themselves, it's not unreasonable that some core-programming were left unchanged even if it wasn't needed - it would be just the way robot-kind had "always done it".
2) The video we see is not the input from the camera or what the terminator "see", but rather the representation in it's "brain" - multiple data streams (eg. from "eyes" and "ears", gyros, &c), data from sensors, status of various systems, errors, damage, &c...
It wouldn't be too far away from how we perceive the world ourselves. We build-up an image in our minds of our surroundings with ourselves in the middle - based on our external senses, but also of internal senses - like position of limbs, pain, hunger. We supplement with experience and memories - like how things are outside our immediate sensory range. And we add feelings like love or hate.
Because vision is our primary sense, much of how we build-up the mind-image will be visual. But we can imagine that other animals would build-up their mind-image primarily using other senses - like smell for a dog, and "radar" for a bat. Still, I would think the resulting mind-image would be very similar to our own - but with for example sources of smell moving around, instead of shapes of light and color.