The venerable script(1) command has been around since 1979 (via 3.0BSD), and while some of the timestamping (supporting via the -r flag to feed the resultant file into the playback) and other utility functions (replay via -p are much newer, the result is the same. Record to a (mostly) text file to schlep around as needed. And it's normally included by default on most installs, including macos.

There's no upload-to-server functionality unlike asciinema, but that may be a feature for some users.