A sound but possibly limited puzzle type. I recommend

• Separating an initial tutorial with explanations from the "actual" challenging levels. The initial impact is that if a snake game is not realtime it must have challenging puzzles; easy levels are "puzzling".
• Adding enemies to avoid, hunt, or herd into doing something. and interesting items
• Adding various snake actions with command keys, like laying eggs (which could reduce snake length but create a target for monsters), spitting at or biting other creatures, activating or dropping items.
• In a significant portion of the puzzles, nontrivially different solutions
• Nicer graphics, Even Pacman is more detailed.
• An undo command to reduce boredom, and a redo command to use it without anxiety.

The idea itself is very creative. You have an excellent novel puzzel game. This is a great time waster and you should make it for the phone. I have to be honest, I played for like 5 minutes and got bored of it on my computer. But that's why it's good for the phone. When you've got a little freetime and don't have access to a computer or console, then these puzzle games shine.

If you want to make it more addictive, incorporate rewards and possibly a leaderboard of some kind. Maybe least amount of moves to complete level. And even though it's a puzzle game, you can have a little story in it if you like. Maybe the snake is on a journey of some sort. You could have different themed backgrounds (desert, grasslands, mountains, etc.)

But the core of the game is novel (at least to me) and that's what counts!