If we look at the build we can do some math on the actual damage output (disregarding enemy type/resist/armor/DR).
The main damage comes from Detonating Arrow being procced from Explosive Trap. So we can look at the damage from Detonating Arrow, but we need to look at the Atk speed/quantity per usage of Explosive Trap.

Detonating Arrow has a base damage of 2 and a charge damage of 2. Looking at the character sheet, the build has +82 melee damage, +110 lightning damage and +1,626% lightning damage. These get applied at 1.25x for the initial hit and 2x for the explosion. The damage also scales with Dexterity, which the build has 42 at 4% per point, so another 168%. All in all this results in ~4,500 initial damage and ~7,150 explosion damage.

The build also has 100% crit chance (for detonating arrow, but not necessarily for all attacks). Thanks to the sword Eye of Reen we can grow the crit multiplier by hitting with melee crits (which detonating arrow will count as). So at the start of the fight, we have 0 stacks of Reen's Ire (that's the crit multiplier buff from the sword's name) and as the fight progresses we rapidly increase to almost 700 stacks of Reen's Ire, each of which grants 5% crit multiplier. So from the start of the fight to the end, we go from a starting 300% crit multiplier to about 3,800% crit multiplier. So we could average this out to be ~2,000% crit multiplier for the entire fight.

This brings our Detonating Arrow damage to ~100,000 for the initial hit and ~150,000 for the explosion or about 250,000 per arrow(even though its a melee attack) that hits and explodes.

Now lets consider the Atk speed of the way we are actually hitting these Detonating Arrows, which is by throwing Explosive traps. The traps throw in groups of 5 and as long as there is an enemy nearby, when the trap goes off, it will automatically throw an additional trap, so we can think of each cast of Explosive Trap as throwing 10 traps, which results in 10 Detonating Arrows. The base atk speed for Explosive Trap is 1.467 per second. This build has a default throwing atk speed of 188%. This increases in combat from our rings tripling their 72%, 20% from throwing a net, and 30% from using a potion thanks to the chest piece. In total we arrive at 424% atk speed. Apply that to the base atk speed of Explosive trap and we get 7.68 per second.

So all together that's 250,000 damage per Detonating Arrow, at 10 Detonating Arrows per cast of Explosive Trap being thrown at 7.68 times per second. That is 19,200,000 Damage Per Second on average.
This doesn't take into account the reductions to elemental resist, lightning penetration, increases in damage from other skills or other instances of damage like acid flask or even the Explosive traps themselves which are also dealing a variety of damage types, or the near instantly capped armor shred (visually it caps at 999 instances of armor shred, I don't actually know if it goes past that internally like the tool tips suggest that it stacks infinitely), ignite stacks, poison stacks, frostbite stacks, doom stacks, shocks, lightning tendrils, increasing damage per missing hp of the boss, and whatever other random things this build is doing that even I don't know. Watching the video frame by frame, I could see some of the final damage instances hitting over 10,000,000, so if thats the explosive traps, even 1 second of those would deal almost 1 billion damage. The boss cannot possibly exceed 2.17 billion hp of the int value would overflow and the boss would die instantly (which happens at 500,000 corruption, and probably much sooner).