Browser version or desktop version? The browser version will save files silently - check the “Downloads” menu of your browser, there should be files like “stacks-<timestamp>.save.txt”. The desktop version will offer the “save file” dialog.
What is your browser, btw? Google Chrome is highly recommended, and Firefox is also a good choice. I have not tested the game with other browsers, so can’t predict their compatibility.
Do a quick test: start a new game, exit the full-screen mode to see browser menus, and click the “export to file” button. Then click “show downloads” or just navigate to “chrome://downloads/” (on Chrome). If there are no files, I will be really surprised.