I see you are trying to set up a really nice high end system. Unfortunately I have some bad news for you concerning your plans.
The first mistake is that the 120" screen is far to big for that room. THX recommends a viewing distance of 11' to 15' ft for a viewing distance of a 120" diagonal screen. Sitting too close to a screen that big is uncomfortable and a literally nauseating experience.
So an 85" screen or less is appropriate if you want more then one row of seats. With a 120" screen that one row will be close to the back wall in any event.
Having corrected that mistake I would not use a projector but a wall mounted OLED screen. A 77" LG OLED will fit the bill fine. The picture quality is much better than from any projector. With that screen you could just about manage two rows of seats. With reclining seats you need much greater spacing than you might imagine. Good theater chairs before reclining are 3' front to back. You need at least 3' 8" to 9" between each row form back to front. So that is almost 7' front to front between each row in the upright position.
I think you need to be about 8' to 9' at least from the screen to the front of the first row for comfortable viewing and any semblance of good sound. So that means the back of the front chair is 11' to 12' from the screen. I actually like to be at least 12' from the front of the screen and even so I like my second row best mainly for sonic reasons.
So the front of the second row is 14' to 15' from the screen and the back of the second row seat will be 17' 9" 18' 9" from the screen upright. Reclined it will be 18' 9" to 19' 9' from the screen which is beyond your back wall. So your back row will not really be able to recline unless your front seats are really too far forward to be optimal.
So ideally that room is a one row theater and two at a push.
The next piece of bad news is that the dimensions of the room are a long way from sweet spot ratios. The biggest problem is that the length and width are too close together. So the room will be inclined to be boomy. Unfortunately B & W tend to tune to higher Q on the bottom end which will exacerbate this problem. Make sure you install the back boxes on the ceiling speakers. Ceiling speakers should not radiate into floor and attic spaces.
So I think this room could be 7.2.4 but there will be little advantage over 5.2.4. If you go with two rows of seats I would definitely opt for 5.2.4.
Now make sure you run all cabling in conduit. Cables can fail and technology changes, so you need to easily be able to replace cables without cutting huge holes in your walls.
The next issue is ease of access. This is almost always overlooked. I would suggest you put racks in between your theater and game room, and allow access to the rear of the equipment from the game room
It is well known here that I really dislike receivers and advise to avoid them where ever possible. Now you have chosen B & W speakers. On the whole I like their higher end offerings especially the 800 series. However B & W persists in making their speakers very hard and difficult to drive, with impedance curves and phase angles that look like the Himalayas. In short they are amp busters, so robust power amplifiers are called for. In addition they tell a big fib about their nominal impedance, but own up to the fib in quoting the minimum impedance. In your case that is 3 and 3.1 ohms for the front set. So the good rule of thumb for the impedance of a speaker is minimum impedance plus 10%. So the impedance of each of your front three speakers is 3.5 ohms at most. B & W really do need to rid themselves of this habit. It is not necessary. I should point out this does not affect sound quality as long as the amps are robust. These are not speakers for amps that are in the least bit wimpy. The rest of your speakers are around 5 ohms or a little greater.
Make sure you follow the Dolby speaker layout to the letter.
So I would use a pre/pro. A Marantz 7705 should do the job nicely. Since this system is mainly for movies I would use rack mounted pro amps like those from Crown or QSC. I would mount everything in metal pro racks for obsessional grounding, hum and buzz avoidance. Also don't forget ventilation. I use a radon extractor fan above power amp case to gently extract air above the amps. I have it on a fan speed control.
As others have stated bi-wiring and Bi-amping is a waste of time and money. Says me who has triamped mains, biamped center and rear backs. However those are actively bi-amped which is a different story altogether. With those low impedance speakers I recommend you use AWG 10 speaker wire at least. You can get Belden wire from Parts Express.
Lastly don't forget protection. This is so often forgotten. The climate is getting more violent and we get posts here from people who have lost the lot due to power surges. We just had the last one within a week or so. So have your electrician install whole house surge protection. This will protect the boards in HVAC, fridges, ovens etc as well. Power strip surge protectors are for the 'birds". Now at the bottom of each rack put in a rack mounted UPS unit that will shave and boost out of range voltages and instantly go to battery if the power is out of bounds. I like units from APC. Power everything except the power amps from the UPS.
Now I have been through this misery twice now. My first home theater on Benedict Lake MN was 22' long by 14.5' wide with 8' ceilings. It had two rows of seats and sounded really very good.
We have recently built a new house and this theater is 29" long and 16' wide with 9' ceilings. Those are good ratios and the room sounds excellent. That just leaves room for three row of seats on risers. You need to raise each row of seats, otherwise view is obscured.
Here is a link to the thread of the new build.
This is what the room looks like now.
Don't forget powering for the seats. You can not get seats that are not powered any longer. Don't forget the rope lights at the steps for safety.
This was the former studio at Benedict MN
As you can see getting two rows of seats was tight.
So those are my only thought for now. My biggest concern is that the screen you propose is far too big for the room. Have fun!