сначала вы пишете mysql
i_query, а потом mysql_fetch_array. Попробуйте определиться между mysql или mysqli.
Либо mysqli:
<?php
$res = mysqli_query($connection, "SELECT videos.* FROM video_category join category ON category.id = video_category.category_id JOIN videos ON videos.id = video_category.video_id");
$video = array();
while($row = mysqli_fetch_array($res)){
$videos[] = $row;
}
?>
Либо mysql:
<?php
$res = mysql_query($connection, "SELECT videos.* FROM video_category join category ON category.id = video_category.category_id JOIN videos ON videos.id = video_category.video_id");
$video = array();
while($row = mysql_fetch_array($res)){
$videos[] = $row;
}
?>