I have two sites running WordPress 4.9.8
On one site I can see “Store uploads in this folder” option on in Media Settings

On another site I cannot see “Store uploads in this folder” option in Media Settings

I am admin on both sites. Why it happens? How to make it visible on both sites? Thank you
While the other answers cover part of the answer (old WP install), it is important to note: The options appear, if one of the options is set. They are stored via the keys upload_path
and upload_url_path
.
Before:

Run (or add directly in the DB)
$ wp option set upload_path foo
$ wp option set upload_url_path bar
After:

As has been mentioned, these options are deprecated and shouldn’t be used anymore.