Here’s some side control submissions and techniques you can do when you’re opponent is on his side (demonstrated on the Submission Master Grappling Dummy)
The first (and most obvious) is going for an armbar from right there.
Typically, you’re opponent wants to turn toward you to escape his elbow to the floor. However, if he turns away, you can follow him, bring one knee over his waist and the other over and in front of his head, and do a straight arm lock on the other side (face down).
The third technique is to go around your opponents head, pin his shoulder to the ground, and lift his arm for a straight armlock.
If he does turn toward you, you can scissor your legs so you’re facing his head, then submit him with a americana/keylock style elbow lock.
Or, you can scissor towards his feet, then switch your grip to the one in the video, and complete with a very powerful elbow lock. Be very careful to go easy on your opponent – it can be quite painful and potentially injure him if you aren’t cautious.
You can also simply wrist lock your opponent right from the initial position of him being on his side.
If your oppponent is defending by gripping his arms together, you can go to the opposite side, then use your knee between his arms to break his grip.
And finally, if your leg ends up between his arms, you can grip your ankle as in the video and submit him with a choke.