The odds are really remote that the new owner of your phone will actually go through the process of using a file recovery utility to restore your old data. And even if this does happen, consumer file recovery utilities are not in any way 100% successful at what they do, and even less so when it comes to just random data dumps. (There are businesses, like DriveSavers, that rely on much more sophisticated and successful processes, but they also charge big bucks so anyone just randomly sending a phone in just to see if maybe there's something or anything on it just isn't a reality.)
That said, unless you actually know (and trust) the recipient when you sell your phone, you just never know where it will end up and who will be the next owner, and that's the issue. So you really should go through the steps to encrypt your phone, and then do a final Factory Reset. It doesn't cost you anything to do this and it greatly reduces the chance, even as remote as it is, that there's anything worth recovering. Once you've encrypted your phone, all your files and such are protected from any casual viewing from an outside source. Without the set passcode, all the data written to the /data partition (where your personal files reside) are not viewable. Even if someone does attempt to use a file recovery utility it won't matter, all the files appear as gibberish because of the encryption.
And just so you're aware, the solid state chip in your phone is a different media than the older, conventional drives that are in a computer. Writing data to the drive might apply to those older, spinning-disk hard drives but solid state memory read and (most importantly) writes data to the actual storage media differently. So recording videos won't necessarily be writing directly over previously saved data the same way as with a spinning-disk hard drive. Also, a Factory Reset does NOT actually do anything like deleting individual files that are saved onto the media. Essentially what this does is wipe the records of what data is stored in that /data partition. So the files themselves are still there, it's just that as far as the operating system is concerned they're now 'considered' to be gone. Conversely that's how a file recovery utility works, it scans a disk block by block searching for recognizable file types. In this regard a Factory Reset on an Android device is similar to formatting a hard drive using a Windows PC, it's not actually deleting each and every file on the drive. All it's doing is essentially 're-labeling' the drive to be wiped clean. A third-party utility like Dban however, does do a secure 'wipe' by going block by block, a time consuming process but very effective. (Every Mac has its Drive Utility that can do the same, a 'secure wipe' option that does a block by block deletion.)