Any Z-code game which is hosted online is using Parchment as the interpreter.
Parchment has a saving issue, but there is a way around it.
On this site, the Zork game is loaded in an iframe with the game running in the Parchment interpreter on iplayif.com. So, to save when playing Zork on textadventures, you have to right-click on the game, hover over "This frame", then click "Open frame in new tab".
In the new tab, enter SAVE. The URL will change. Copy your URL and save it in a text editor. Now, you can open your browser, paste in the URL and go. Your game is now resumed.