Hi everyone, I'm the Oren Jacob in the video. Hopefully I can offer some first person color commentary about the video above that might serve to answer the questions here. Note, after 20 years at the studio I left Pixar last year to start ToyTalk (www.toytalk.com), so this answer hasn't gone through any PR filtering, it's straight from my foggy memory of those events back in the late 90's.
First, it wasn't multiple terabytes of information. Neither all the rendered frames, nor all the data necessary to render those frames in animation, model, shaders, set, and lighting data files was that size back then.