Cool idea. I also like the similar "observing game" on chess.com - although this has more of a time element in it too.
How to "game" works for those unaware is you go into live chess and watch other player games (usually friends and ideally stronger players than yourself, but they don't have to be). While they are playing their game live, you can actually "predict" their move by playing it on the board. chess.com counts how many moves you guessed correctly and incorrectly. It then compares your "score" to others watching the same game. Sometimes it is fun to do alone and other times it is fun to do with popular games so you can "compete" with other observers in a way.
That can be fun and interactive; plus, you never risk your own rating because you aren't actually playing the game. You can even observe someone playing against a GM and it almost feels like you are playing a GM too
Solitaire chess is a great way to improve your game and there is free software on the internet available that conveniently lets you play solitaire chess. But it can sometimes get boring. I have found a more interesting way of playing solitaire chess. Find chess videos that analyze chess games move by move, this website, chess.com, has many such videos as does YouTube and many other chess andd video sites. Play the video normally but keep your cursor on the stop button. When the first move is made in the video stop it and try to figure out the best move that the opponent can reply with. Then play the video so you can see the selected move and listen to the commenter's comments. Then watch the next move and so on. You can do this with any of the available chess videos. You should use ones using the games of your favorite players. For example I like Paul Morphy, his games are tactical and exciting. Or you might want to watch Tal's games and see why he was called "The Magician." Or perhaps you might choose Bobby Fischer's games. The choice is yours, have fun!