Would ESD damage my motherboard easily?
Had you said "Could" instead of "Would" and left off the word "easily", I would have said, "Absolutely! ESD can damage a motherboard".
Manufacturers over the years have built in many ESD damage mitigation techniques to greatly reduce the risk. But there is no way those can eliminate possible risks complete.
That said, looking at your picture, it seems you touched the PCB edge and I "suspect" the ESD you sensed was the voltage jumping to the motherboard's ground plane - by far, the safest place to jump too.

After all, circuit cards should be handled by the edges.
I say, press on and use it. I would bet it will work fine. But from now on, especially when handling sensitive devices like the CPU, RAM modules and cards, try to remember to touch a grounding point (bare metal of case interiors are good) before reaching for the sensitive device.
Using no ESD equipment is acceptable for kids who build their first computers and are not aware of.
"Acceptable"? ??? Ummm, not the word I would use.
Common? Sadly, yes.
Most professional manufacturing and repair facilities use proper ESD equipment. Not only do they use it, but they perform regular testing and maintenance to ensure it remains effective.
Everyone should be aware of the risks and if careful and disciplined, the occasional home user does not need special equipment. They just need to remember to discharge any static BEFORE reaching into the case or for any sensitive device, and discharge again frequently thereafter to keep new static from building up in the body. After all, just squirming around in our clothes can build up destructive charges, especially in low humidity environments.
BTW, dogs don't appreciate you discharging the static in your body on their wet noses.
My
bold underline added below,
ESD plug + wire (which needs to be replaced regularly

I think this a critical point WAY TOO OFTEN overlooked or ignored, that should be emphasized more often.
This is especially an issue with ESD wrist bands. Sweat, dead skin, dirt and other contaminate will quickly degrade the bands ability to drain off the static from our bodies. And sadly, if the user is used to relying on the band alone, that can result in ESD damage anyway.
So if one uses a band, then I agree 100% and they should be replace regularly - even if they "look" perfectly fine.
should I worry about it after if it even works properly?
Not "worry". Just be aware of the possibility and remember to discharge yourself before reaching in.