Ah, ok. Weird, but good to know. (I've had audiobooks from a couple sources actually download as MP4s before, and the result was a bit unpredictable, so I thought I would eliminate that possibility first. Like I said before, I'm spit-balling here, just trying things out by eliminating what the problem ISN'T so we can narrow in on what it is.)
I don't know if you have access to a Mac. I do, but I can't do very intensive stuff on it, which is why I've been using my PC for a lot of stuff lately. But there are a couple Mac apps that really help when analyzing these files.
I looked at your file with a Mac app called Yate. When right-clicking on a file in Yate, you have the option to display a raw data log, which basically shows you the layout of the atoms (or frames, if the file is MP3) with nesting.
This is your original file:
ready_player_two_raw_data.txt (3.4 KB)
As you can see, the moov atom has three children. Two of them are trak atoms, the third is a udta atom.
The first trak atom is your audio track. The second is the text track within which the Quicktime chapters are stored (in a really convoluted way that isn't fun to parse.)
The udta atom (which also stores your metadata) has a child called chpl. This is your Nero chapter list.
Using another Mac app called Subler, you file looks like this:
Highlighted, obviously, is your text (chapter) track. Since Subler is meant as a video tool as well as audio, it mostly deals with the Quicktime chaptering. But if you delete this text track, it will also delete the chpl atom.
What I've done is export the chapter data as a text file, delete the text track, then re-import the chapters. This rebuilds the Quicktime chapter track, but NOT the chpl atom. Upon doing a save-as, it also optimizes the file (restructures some of the atoms to get rid of unnecessary redundancy and compact padding where available.)
ready_player_two_rechaptered_raw_data.txt (3.5 KB)
So here is your file with ONLY Quicktime chapters, instead of both. If LAP reads Quicktime chapters, it should read these. If it doesn't, then your issue isn't what we assume it is.
Note that doing all this was a really quick process (like, less than a five minutes, it's taking me way, way longer to write this reply.) Once I exported the chapter data as a text file, I opened it with XCode (which has a much superior Find/Replace functionality) and did the following replace before re-importing the chapter data:

# is substituted for an option XCode allows when using Find/Replace for any digits, so this search replaces the leading zero in all the chapter titles at once.
Try downloading the result and seeing if it works for you.
If so, and you have access to a Mac, Subler is available for free and might be a solution if you only need to do a few files.
If you don't have access to a Mac, download Drax and export your chapters (either way will work, as Subler recognizes both) as text files. Edit the chapter titles to what you want them to be, then PM me with links to the chapter text documents and files you want to apply them to. I can run them through Subler super quick and the whole thing can be done in way less time than it's taken us to have this conversation.
ETA: Upon further experimentation, I've discovered that if I take the file I rechaptered with Subler on my Mac, the Quicktime chapters Subler wrote are read by Mp3Tag, and if I make a minor edit and save in Mp3Tag, it will have both Quicktime and Nero chapters, and both will be accurate/edited.
So, if all else fails, whether you have a Mac or take my offer as stated above, you can export, delete, and re-import the chapters in Subler, then so a small edit in Mp3Tag, and you will have chapters that are accurate in both LAP and Mp3Tag.