Anio,
You can use a dial caliper to measure the diameter of the hub inside the slot, but you can cheat a bit, there. You can bend a heavy paper clip straight, then bend it into a "C" shape, larger than the hub at the slot. The points of the "C" will be the measuring tool. Bend the "C" open, far enough that the points go into the slot, and just barely touch the metal at the bottom of the slot. The points of the "C" should not spring open wider to do this, and both points of the "C" must just touch the bottom of the slot at the same time. Ask questions, if needed, here.
Then, being careful not to bend the metal, place the points of the "C" on any ruler or measuring stick, and record the measurement. A Metric/Imperial steel tape-measure will give you the measurement in Metric and Imperial units. This tells you the size (diameter) of the snap ring slot, at the bottom. Take the old snap ring to a good auto parts store, and have them sell you a snap ring of the correct diameter and thickness to fit the bike hub slot. Chances are, it will be a Metric part. Buy a pair of snap-ring pliers (which your free "help" did not use), and install the new snap ring on the hub as it should be. The auto parts store can show how the snap-ring pliers work, if needed.
I believe the snap ring is important, so do not run the motor (or bike) without it. They never put such things on machinery just as a useless decoration. The function of the snap ring may be vital to the motor or associated parts. Do not go without it. HTH.