It's hard to give an answer without any of the situation (videos) you refer to provided, as there are many ways to avoid ESD damage. The most important: don't wear plastic/gummy soles and clothing and handle slowly with care. Also, most consumer devices, like consoles, aren't as sensitive. Next, while older technology is more prone to ESD, especially old CMOS, more modern - and that starts already in the 1980s, are well protected against most ESD situations. So when handled with minimal care, chances for damage are very slim.
They never touch a radiator or mention using some kind of technique or measure to get rid of the static electricity in their hands/bodies.
But this is super important when you open up a computer.
No, it isn't. Today even less than back in the days. As Justme already pointed out, Touching a radiator only matters if that radiator is at the same (ground) potential as the device you're working with.
Is there something about old consoles that make them immune from this threat?
Kinda. Most devices aren't connected to a common ground at all. This is especially true for home computers and consoles. Essentially all devices that operate from a two prong mains plug (*1) do not carry a common ground with any radiator or whatsoever.
A device not connected to any ground potential, to which the handler is as well connected, can have any potential. It doesn't matter. It could be at 15,000 Volts against ground and still work fine. That's why power lines can hang nicely between poles without shorting. It's the same reasons why birds can sit on high power transmission likes without starting to glow.
So unless a differential potential is created, nothing will happen.
It's about ESD (Protection)
ESD or ElectroStatic discharge is when two potentials equalize - ever felt that spark when touching a door handle after going over some plastic carpet? Jup, that's ESD. Notable here, it happens despite the door handle being not grounded at all (*3). Why? Because it's all about equalizing potentials, not connecting to a certain potential.
And that's the most important reason why usually and most the time nothing happens when people handle old electronics in videos. They carry the device, put it up a table, open it etc.pp. During all these actions the potential between the electronics on the inside and the handler do equalize. Slowly and in a harmless way.
Which is the second point there: Damage is not caused by voltage (otherwise above birds would again be fried) but by current. Thus, if equalisation happens slowly, next to no current flows, but electrostatic buildup is removed. That's also why ESD bags aren't good conductors but bad insulators (*4)
So the task is to (slowly) equalize potential and keep it that way. This can be done by careful handling, supported by tools. That's where, for example discharging mats, wristbands and connections in-between come into play.
Whatever needs to be handled gets placed on the mat - still within transport packaging. The handler wears a wrist band connected to the man, and after unpacking the device as well gets wired up.
And that's why my workplace setup consists of two quite classic Knürr Elicon tables:
(Picture taken from their Brochure)
No, mine are just basic grey ones, without the integrated add-ons, but more shelves (*5). Not cheap but all worth it. All components are grounded, the tables are covered in discharging surface. All connected to a common ground, including my chairs. Essentially no chance to build up a potential.
Whenever handling a device it gets put onto the table and sit there for some time after connecting to the tables potential. There is essentially no chance to build up a potential.
Having said all of this, in most real world situation it will work fine without additional tools, by simply acting sensible.
*1 - There are certain configuration where it still could be, but these are rather rare and confined to certain states/regions/networks.
*2 - Still have it. Please don't ask for details or pictures.
*3 - Dry wood is a rather acceptable insulator.
*4 - Meaning they have a moderate to high resistance, allowing a potential to discharge slowly, so whatever is inside gets slowly adapted to whatever is outside with next to no current flow, thus no damage.
*5 - Again no, there are neither in such a nice room, but a dark attic, nor are they clean. Rather cluttered with electronic waste, documentation and tools :))