I have my 2 cents to put in on this topic.
From the screen shot of the forum, the vBulletin version is 4.2.2. We are running vBulletin version 3.8.4. They are one major version apart, which can be significant.
vBulletin uses a MySQL database to store data. It's a relational database, so similar data can be stored in its own entity (tables). I don't know the architecture of the vBulletin database, but a simplified one might have all the posts populating one table, thread information in another, forum information in another, member info in another, etc. There are established relationships between the tables so that the vBulletin software can retrieve the data and organize it and present it on a browser.
Even if we were to get only the database for AFI, the chances are very slim we could do anything with it, such as merge the history into AAm. The database structures most likely changed with the version upgrade. We would have to migrate all the user information and their security settings. Given enough time, it could be done, but the level of effort would be very high.
The only viable option in my opinion is to buy the whole site from the latest backup. We would have to host it somewhere and rebrand it or leave it as AFI. Who knows if the owner still has a backup, but I have a feeling he did not just delete it permanently.