The ChatGPT desktop client carries everything it needs to open documents on its own machine. A dig through ~/.cache with OmniDiskSweeper turned up 1.7GB in a folder called codex-primary-runtime, left there by OpenAI's Codex desktop app, since rebranded to just ChatGPT.
Inside sit a full Python installation, a full Node.js installation, and native binaries for Poppler, git, and the LibreOffice office suite. The runtime's documents plugin folder holds the skills that tell Codex how to find and use those binaries.