First photo is the clutch cable.
Second photo is the clutch release arm.
Third photo is the clutch hand lever.
Any quality bicycle brake cable can be used as a replacement for your broken clutch cable.
In fact, most brake cables sold at bicycle stores are much better quality that the cable that comes with the engine kits. Try to get one with a teflon liner inside it. It will greatly reduce the effort required to operate the clutch.
If you can get a teflon lined cable, do NOT oil it! It does not need any additional lubrication.
The installation of the cable is pretty much straightfoward. If you can thread laces into a shoe, you can change the cable.
Scroll down to Step 4 in these instructions if you want to:
2-Stroke Engine Kit Installation