SSH, once you (verify and) accept the first key exchange cannot be tampered with in transit, nor have the contents viewed by those sitting in-between.
However, I believe everyone's stdout/stderr is available to everyone, if everyone is the same user, and if that user has read access to /proc, so that confidentiality is only restricted those who access to the server.
This is actually just a Go app which implements SSH using the Go standard library's SSH module. It's not like you're really SSH-ing into a server. See the source: https://github.com/hackclub/jobs
In "public access single-app" cases like this, the user is generally connected to a restricted shell or other program which (… supposedly—this is very easy to get wrong if you're running anything that isn't specifically built for it) does not allow arbitrary executable access.
It's also relatively trivial to set something up like this as SSH server supports auth delegation using PAM, and PAM can be configured with a single line using pam_succeed_if.so to disable auth only for a certain user.
However, I believe everyone's stdout/stderr is available to everyone, if everyone is the same user, and if that user has read access to /proc, so that confidentiality is only restricted those who access to the server.