I recently bought a Monster Joe 80cc ATV for my son. It does not have spark. What should I check/replace?

Pics with the plastic body removed:

 

I think it was made around 2005. I heard it is a copy of the Raptor 80cc. Is this true? Pics of the engines on the raptors do not look the same.

 

here's a start: check the brake light switch for a safety interlock. does the brake light switch work? do you hear a "tink" at the left handlebar? your brake light may not work due to a faulty wire or bulb, but you should still hear a "tink" in the switch when activating the lever.
have you checked all of the quick connects on your wiring harness? make sure they're making good contact and check the wiring coming in/out of them?
spark plug ceramic cracked? checked your coil wire up to the coil for cracks and deficiencies?
does your key-off/on switch actually work?
does it have a tether shutdown switch at the rear and under the seat?
you're going to need a multimeter/ohm meter.
that'll get you started.

 

The taillight is missing. Two bare end wires at the rear. It does have a tehter - looks to be bypassed - has a wire connector connecting both wires together. Key switch does work. The engine turns over when activating the elec. start. I do not see a spark when I pulled the plug.

 

You have a GY6 style engine.

You don't "bypass" the tether by shorting the wires together. That "kills" spark. Remove that jumper wire and leave the tether switch unplugged from the main wiring harness. Then see if you have spark... If not we can look further - but a shorted kill switch wire (as you described) is wrong and we need to fix that first.