Pool table with a dining table topper for the few times per year when you need an extra table.

Newer/modern pool table styles are less bulky than the traditional styled pool tables most of us grew up with.

Its important to have a formal dining room! Definitely dont get rid of it. Have you considered turning that free space into a Parlor for guests (a fancier lounging area meant to entertain) or a Parlor+Tea/Coffee room with areas to brew coffee and tea, as well as tables/sitting areas to socialize and enjoy that coffee/tea. Like a miniature coffee shop and lounge area that you could also add board games, etc.

Where is the dining room? Through the opening on the right? At first glance there are a couple of things that stand out. 1. The table near the kitchen area is facing the wrong direction. 2. if the dining room is where i think it is then it is its own separate entity and placing a table off the kitchen is fine , however I recommend changing shape. Rectangular in the dining room and round in the ktichen so you're not repeating. Then a family room or "hearth room" seating area focused around the fireplace. Area rugs and lighting will differentiate each space from the next. I would add a chandelier over the kitchen table and I would anchor the fireplace area with an area rug and i would anchor the "formal" dining room area with an area rug as well. Last if you are planning on doing anything construction wise to this home I would redo your fireplace. Something like this.

If people already stand and eat near the kitchen, I'd put the table next to the kitchen and use it every day. Then turn the formal dining room into what you're missing, like a den, an office or a play room. A round table keeps the walking paths open and feels less crowded.

I would keep the dining table in the dining room and maybe add an additional island with stools to that large area near the kitchen. I see you already have a few stools, I would put another island adjacent to that so it's like one large, less formal, eating area.

Do you really think you would use a formal dining room? Most of us usually eat much more informally nowadays - as you have already noted in your post. . If formal entertaining professionally is needed then yes, a more formal room might be needed, if not, then use it as a quiet space away from the TV,

It is the kitchen design space that is messing up with the entire space.

The kitchen floor should have been installed at least to the end of the cabinets. New build, possibly the floor could be replaced with the tiles. While builder is there he can rebuild the island so you don't need a formal dining room. Poor design in the first place and worth the money, in the long run, to fix it. Something on this idea and you can keep the sink/faucet.

As for the funky dining room idea, when blinds are open, where does the door lead?

You could do a lot with this space. Grille outside, casual dining