When discharging to the chassis frame, you're "shorting" the capacitance built up within the tube.
Basically, you're shorting the + anode inside to the - cathode outside.
You're NOT shorting it to "ground" or "neutral" with respect to the mains (AC) outlet..
In fact, since all arcade monitors are isolated from ground & neutral through the use of an isolation transformer, even if you DO have it plugged in, you still don't have a "straight line" to ground/neutral.
[And think about it... even if you could short it to ground/neutral... do you want a 22 Kilovolt zap travelling through you're home's neutral line on the AC until it hits ground outside your house on the transformer?
? Probably not!!!!
]
Basically, just think of the picture tube as a big massive electrolytic capacitor.
One lead is + (the anode cap, that leads to the capacitance charge plate on the inside of the tube), and the other is - (the outter glass plate on the tube that *should* have a ground wire wrapped around it!).
When you short it, you remove the capacitance built up between the plates, just like shorting 2 wires of an electrolytic capacitor. You don't dissappate an EC by connecting the + lead to your AC wiring ground or neutral... you just disappate it to the - on the capacitor itself.
If you search google you will find some people claiming that if you dont slowly discharge (through a resistor of some type), you will ruin the tube. Others claim that's hogwash and leaves you more susceptable to a lingering charge that never disappated, and can still hurt you.
The choice is yours... believe who you want. I always have just grouned it out to the frame (that is electrically connected to the outside of the tube--always checked with an Ohmmeter before I do it), but never had a zap, as the discharge circuitry was already working and no charge was still in the tubes, but you need to always be careful and never assume. I trust what Bob says so I go with the quick zap route.
Be safe!