SOLVED
I incorrectly assumed that the droplet came with a pre-built and pre-configured ossndb database. This was not the case. I accessed mysql and created the ossnb database with ossndb user and it worked. For anyone else having this issue, this is what I ran to solve the problem:

> mysql -u root -p
mysql> CREATE DATABASE ossndb;
mysql> CREATE USER 'ossndb'@'localhost' IDENTIFIED BY 'password';
mysql> GRANT ALL PRIVILEGES ON ossndb.* TO 'ossndb'@'localhost';
mysql> FLUSH PRIVILEGES;

Once I got to the page shown in my previous post's screenshot, I entered the database name, database user, and password, website name, and email addresses, and proceeded. Everything worked after that.

> I guess you miss the concept, you don't have to run these commands or
> do anything. Please see
> https://www.opensource-socialnetwork.org/wiki/view/3235/how-to-install-open-source-social-network-on-digitalocean
>
> Now i guess you have also installed and changed database details? Such
> error is sql error. Please delete your droplet and create new one and
> follow exact steps above. And on step 9 wait for few minutes. Then
> follow the instructions, and do not change already filled database
> settings, you only have to add your email address, notification email
> address and website name,

I didn't run any commands. I created the one-click OSSN droplet and immediately navigated to my IP in a web browser. From there, I followed all of the steps from that link you provided. I did not change any of the database information. Literally the only thing I changed was the Website Name and email addresses and it shows me that No Such File or Directory error.

I guess you miss the concept, you don't have to run these commands or do anything. Please see https://www.opensource-socialnetwork.org/wiki/view/3235/how-to-install-open-source-social-network-on-digitalocean

Now i guess you have also installed and changed database details? Such error is sql error. Please delete your droplet and create new one and follow exact steps above. And on step 9 wait for few minutes. Then follow the instructions, and do not change already filled database settings, you only have to add your email address, notification email address and website name,

Please follow the steps as explained in
https://www.opensource-socialnetwork.org/wiki/view/1101/how-to-report-a-bug-error
and provide the error.log of your webserver.

Original screenshot link didn't work, so here it is: