Solution: House of Games
Answer: STAR WARSAW

Written by Adib Surani

The most important step of this puzzle is to recognise the game show as Richard Osman's House of Games. If you're one of the lucky ones who have actually caught it on TV, you'll probably recognise it from the framing as well as the individual games. Otherwise, a quick google search for "House of Games" or similar would suffice.

The way the game is played is there are five rounds per episode: the first round is picked randomly from a set of "Round-1-only games" and so on up to Round 4, and then Round 5 is always Answer Smash. This per-round grouping isn't reflected in the Wikipedia link above, which groups all the games by the "type" instead. Nevertheless, the matching of the games from the list should still be relatively straightforward.

Each sub-puzzle plays one of these games to produce an answer with a number or ordinal, which we can then index into the name of the game. The full list of games and answers is as follows:

No. Answer Game name Letter
1.1 The Sixth Sense Cine-Nyms Y
1.2 Nintendo 8 Sorry, Wrong Number O
1.3 Three Kings Hidden in Plain Sight D
1.4 Fantastic Four The Answer's in the Question A
2.1 Snow White and the Seven Dwarves Totes Emoji M
2.2 Covid-19 Build Your Own Question O
2.3 12 Distinctly Average V
2.4 George III Stick It I
2.5 Eight Elvises All in the Details E
3.1 ...Baby One More Time Pop Art P
3.2 Three Little Birds Broken Karaoke O
3.3 Maroon 5 Vowel Movement L
3.4 Big Hero 6 Opposites Attract I
3.5 Twelfth Night There Once Was A Quiz Show Host Called Richard.... S
3.6 (Biw)Eight Midcorrelation The Elephant in the Room H
4.1 Six Nations Championship The Nice Round C
4.2 Ruyton-XI-Towns Where Is Kazakhstan? A
4.3 First Base Put Your Finger on It P
4.4 The Second Best Exotic Marigold Hotel Size Matters I
4.5 10 Downing Street The (Not Quite So) Nice Round T
4.6 All children, except one, grow up. And The Answer Isn't A
4.7 9 AD I'm Terrible At Dating L

Each row on the roof then spells out a single word:

House of Games roof

The final step then is to smash these together: YODA MOVIE = STAR WARS, and POLISH CAPITAL = WARSAW, and these get smashed into the final answer STAR WARSAW.

Author's notes

This is one of my favourite quiz shows (along with Only Connect), which I enjoy so much I wanted to share it with the rest of the puzzling world. My personal favourite game is Broken Karaoke -- unfortunately the extraction mechanism restricted my choice here and I was left with a song that many people probably might not recognise: Bob Marley & The Wailers - Three Little Birds. I tried to do it justice by timing it properly, at least.