So, a lot of people (mostly on steam) seem to suggest using the "Locate Game" feature, but in my case (and I believe everyone here) this is NOT an option. The button simply isn't there unfortunately, but I really wish it was. There seems to be no "easy" way to tell Origin where the game is. My game is stuck in the "Download" state, with no options beyond setting up cloud saves, favoriting/unfav, hide, and download.
Having said that, I have resorted to digging around Origin's files and folders to figure out if there is a way to force it to locate the game outside the application interface.
So far I have found out that, after installing, regular Origin games (like the Battlefield 4 I have) create entries in the Windows Registry (press "Windows key+R" and type "regedit") which contain data such as their name and installation folders, among other types of information. Titanfall 2 didn't create one such entry, not only that, it creates an entry with the Steam application ID (ID:1237970, it's located in the same group of entries that regular Steam games use (which makes sense to be fair). I couldn't find a Titanfall 2 entry in anything related to Origin in the registry, but I'm not sure this is supposed to be like that since Steam handles the installation, maybe if someone who got the game to run properly could test this out and tells us what they find.
I also checked the %appdata% folders looking Origin log files and found out 2 logs that shed some light into what happens behind the curtains, the log files are located at:
1 - EALink log: %AppData%\Local\Origin\EALink\EALink_Log.txt
2 - (Origin) Client Log: %AppData%\Local\Origin\Logs\Client_Log.txt
The first log seems to show how Origin calls the EALink application with some parameters (Steam client and game app ID), and seems to be successful (maybe it's just an online component). It does seem to manage account linking or somesuch.
The second log shows Origin performing a download request for the game, but with missing name parameters (it just says "Unidentified Game"), but I don't know if this is on purpose (since Origin seems to refer to TTF2 by its app ID), and it seems to forward the download request to Steam (which had already downloaded the game beforehand). During the launch process, there is an "RTPFlow:attemptGameLaunch" step which comes up with an error which prompts Origin to display a dialog (which I believe is the error window with the "game not installed" message). The error it reports is "R2P error", and I tried googling that up but I couldn't find anything useful. I guess that's probably too internal, and something that only EA support or someone of the sort could answer.
Anyways, I attached screenshots of both logs below, and I'll keep digging around for a fix. I'll post again if I find anything interesting or useful.