Non-downloading games will save your progress, but whereas you play your game online, you don’t have to store the bulk of the game in your computer so it saves more space than downloading a bunch of free or paid games. You then don’t have to deal with a bogged down computer with a bunch of crud attached to your free computer games. However, you must learn to clean your cache to remove unwanted cookies and the such as a result of playing games or after the end of the day when you have visited any websites.
The games I have listed above are available on line to play in your browser so no downloading is required. However, you may be asked for your name, age, or e-mail address to sign up for the game so you can verify who you are and that you are of appropriate age to be playing as well as to give you a log-in that you can go back to if you lose your password and sometimes you are required to confirm that you really signed up through your e-mail, too, which verifies that you are you and not somebody else using your name.