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Does the `watched_videos` column contain `unique_id`'s? Are these numeric or string IDs? (If they are string ID's you shouldn't quote them below!)

Also, why not use the `$exclude_list` you already made? Did you print the queries and tried them manually, and do they return what you think they should? 

Also, your SQL will be invalid if the `watched_videos` array is empty.

    // Generate a comma-separated list of unique_id values to exclude
    $exclude_list = "";
    if (!empty($watched_videos)) {
        $exclude_list = "NOT IN ('" . implode("', '", $watched_videos) .      "')";
    }

And your SQL lines:

    // Select two random videos from the "less_videos" table, excluding watched videos
    $sql_less = "SELECT video_id, description, points FROM less_videos WHERE unique_id $exclude_list ORDER BY RAND() LIMIT 2";
    $result_less = mysqli_query($conn, $sql_less);

    // Select ten random videos from the "more_videos" table, excluding watched videos
    $sql_more = "SELECT video_id, description, points FROM more_videos WHERE unique_id $exclude_list ORDER BY RAND() LIMIT 10";
    $result_more = mysqli_query($conn, $sql_more);

It's also a good idea to sanitize anything that's going into another SQL query, no matter where it comes from.