Why does my stem have no bolts?
You have an older type of stem that is used with a 'threaded steerer' fork.

In this system the fork is held on by the large nuts on top of the head tube, the stem is held in the steerer tube with a wedge that is tightened by the bolt on top. On newer, now much more common, 'threadless' steerer systems the fork is held on by the stem clamping the steerer tube.

If the fork is moving in the frame the headset bearing need adjusting. If the stem is moving it need to be tightened (I suspect the former as you say you have tightened the stem bolt already.)

Here are a couple of videos that deal with threaded steerer systems:

Adjust The Bike Headset On A Threaded Steerer

Adjust A Bike’s Handlebars Attached To A Threaded Steerer