SQL databases are internally organized in files, but these files have a lot of indexes for super-fast data search.
Imagine you have 10000 players on the server and somebody is trying to login. In an SQL database the table containing usernames can be immediately accessed and the name can be found via an index. Not to go into too much detail, but lots of SQL database system use an index with letters if the searched field is of a text type. That means that the username "Alpha" would be search by first finding the index for A (which is 1/26 letters), then the next linked index for L (which is yet again only 1/26 and it's only that high if all other letter entries actually exist) and so on until it gets the text ALPHA together. At this point the index points directly to the entry in the database containing all user information with only 5 * 26 = 130 reads (worst case scenario).
In a normal file you would have to go through 10000 user data entries to find that username and the worst case scenario is that you have to go through all of them. Not to talk about first finding the part of the data that is actually related to user data (not save data, ip logs, etc.) It's true that such a file could be split into several files and indexes could be added in there as well, but SQL already does that and so much more. What if 2 players try to save some data in the same file? One of them would have to "wait" until the other one finishes or they could corrupt each other's data. SQL databases also handle the problem of concurrent access.
There are even more advantages, but there are literally books written on this subject so I will stop here. If you are interested, you can always google a bit. It's quite an interesting topic. I even had two classes back at university all centered around SQL database systems.