The puzzle has three components:

1. 12 passages, each followed by:
2. A phrase, indicated by blanks and a door icon. In each, one blank is marked.
3. An SAT analogy style phrase, marked with blanks.

Based on the title and flavortext, the solver should recognize that this is a room escape related puzzle. Upon reading through the paragraphs, two things should become apparent. First, that each paragraph is alluding to a specific media property. And second, that the paragraphs are out of order. The solver may start identifying some of the allusions, but will notice that none fit into the blanks at the bottom.

The key to those blanks is that every section of the room escape walkthrough refers not only to a media property, but to a specific room within it, that is always explicitly named. So, in the example of Harry Potter, that’s the Room of Requirement. The door symbols stand in for the word “room” in each ID. This is additionally clued by the Rumi (ie Roomy) quote in the flavortext.

As the solver starts to fill in room identifications, they may notice that they’ve been listed in alphabetical order (the 4 that begin with the door symbol could be a tip-off). Given that the narrative’s order has been scrambled, the next step is to find the correct order for all rooms.

There are a number of clues throughout as to ordering. One path to putting the rooms in order would be as follows:

1. 2 is clearly the first room, what with the timer starting to count down.
2. 6 must be the last, given it contains the escape.
3. 4 begins with the protagonist soaking wet, so it must come second, after room 2 flooded.
4. 6 comes 9 rooms after 8 (based on the use of the rat), so 8 must be 3rd.
5. 7 comes after 1, because the protagonist can walk again, and his muscles are sore.
6. 2, 4, 7, and 8 were the physically uncomfortable rooms. 7 follows a comfortable room. So 10 must come 4th, after 8.
7. 9 must follow 12, given the elevator dinging open (this is the only thing that would plausibly ding at the beginning of a room).
8. There are only two rooms (10 and 12) that involved descending through the floor. 12 is followed by 9, so 1—which indicates the character left the previous room through the floor—must follow 10 and come 5th. This also places 7 at 6th (see step 5).
9. In 12 the protagonist looks at his watch and sees that he’s just over halfway. (Also, this section starts “another empty space”—naturally following 7.) So 12 is 7th, and 9 is 8th (see step 7).
10. 5 must be five rooms after 1, from the allusion to “tame, muscle stiffening lasers.” This places it 10th.
11. 11 alludes to there being no human actors in the past four rooms. This is only possible in position 11.
12. Leaving, by process of elimination, 3 in the 9th position.

There are additional clues in the text, including use of items and allusions to how much time is left. Here is a full list:

Extracting letters from the blanks is a clear matter of taking the red blank in each ID. Ordering by the sequence in the escape will give the string BOOTBITTHESE. The solver can then place these words in the analogy at the bottom of the page to get BOOT : BIT :: THESE : ? (Boot is to bit, as these are to ?). “These” are ROOMS, so applying the transformation of turning a double O into an I transforms ROOMS into RIMS, which is the answer to the puzzle.

Table of all IDs, Room names, and order: