Asciinema is described as 'Record and share your terminal sessions,the right way' and is an app in the OS & Utilities category. There are six alternatives to Asciinema for Linux, Mac, Windows and Online / Web-based. The best alternative is Scrimba, which is free. Other great apps like Asciinema are showterm (Free, Open Source), terminalizer (Free, Open Source), ttygif (Free, Open Source) and ttyrec (Free, Open Source).
ttyrec is a program and/or its file format capable of recording the TTY output of a text-mode program together with timestamps and then replaying it. It is widely used for example in the NetHack community for storing game replays.