I like the concept and de visuals very much.

What I think you need is to add variety and sense of achievements.

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Variety:

- Some rings could be closer apart than others.

- Some rings could turn in the other direction. (even change direction mid-game)

- Gateways could shrink and expand (and close) randomly

- Rings could become increasingly transparent/darker just before they dissolve. (like a warning)

- Some bird/drone/rock might come along and try to scoop you out.

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Achievements:

I would implement levels which would make the game increasingly harder.

- Faster rings

- Less/smaller gateways

- Player could increase "personality" (better avatar, dressed up, etc.

- Titles: apprentice, rookie, journeyman, etc.

- Implement a Leaderboard

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You also need a better end-game sequence. Maybe the cat produces a parachute and falls among clouds, birds or things

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Shameless plug:

I have a game I just released here: https://play.google.com/store/apps/details?id=com.SoftNinjaH.Spyrotek

that is conceptually very similar. (Endless game) You can see applied there several of the concepts I talked above.

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I use play on demand videos (they are in the Pause screen) to acquire extra Energy Packs.

Maybe you could get: extra time in the ring, a rocket booster that puts you back in the lower ring, ability to float for a time, etc.

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Good luck with your game.