Are these all OK?
Let's continue our game.
Let's continue our program.
Let's continue our trip / journey.
Let's continue our chat / talk.

Question

Answer

I'm excited to learn more about it. I like to spend my free time playing the game. The game is really very addictive. And I would love to continue it by following the original link https://topcasinosreviews.in/casino/paripesa/, then the game is safe. I found this review on a verified platform. You can check it out.

Answer

The game is really very addictive. And I would love to continue it by following the original link https://topcasinosreviews.in/casino/paripesa/ , then the game is safe. I found this review on a verified platform. You can check it out.

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Yes!  Well done.

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All of these are correct.

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You can use the -ing form as well: 
Let's continue chatting/talking 
Let's continue watching the program/playing that game ("let's continue our game"/"let's pick up from where we left off" would be fine too, left off= stopped) 
Let's continue our journey/trip sounds fine!