There are cocktail tables that can be raised. .....Seems quite a small area for what you're attempting. Add more pictures of the rest of your space, and dimensions of the lounge would be helpful.....

Yes there are many coffee tables that raise up to become dining height . Please take that stuff off the wall above that sofa put it where the art is and the art where those shelves are . Google adjustable coffee tables that become dining .

If you do get a coffee table that can be raised you will need extra chairs for seating for four people.

Sitting on that sofa scooting up to a raised coffee table would be horrible for backs. No one would play long. And no there is no way to play a game while lounging unless it's a video game of some sort. Show us more of your space. There needs to be room for a proper games table.

If there is a dining area that is the answer. Comfortable chairs and you're set.

We have the wood version of this: Arhaus. Apparently they don't have it anymore, but something similar?

As usual Patricia has the right idea.
The open shelves filled with doodads above the sofa kinda intrude on any relaxing feel.
Even if there is space to safely recline your head,the overall vibe is off..."dont lounge here,stuff may fall".
Put something flat there...painting,tapestry,etc.
To properly play cards or board games you do need a table and chairs that allow you to sit upright.

I disagree with others negative comments and think this is a cozy room. I would be happy to play cards here. That said, I prefer sitting at a table when playing cards in general…

Thank you everyone for your suggestions and comments. I appreciate your advice.