Is the Mechromancer / Gaige's Zapper Class Mod description text wrong? How exactly does it work?

Solution 1:

The effect of the mod is to increase all shock elemental damage over time by some percentage (the first 29 on your image), while also increasing the chance of any given attack triggering a Damage-Over-Time effect by some percent of its base percentage (the second 29). So, a 100=damage attack with a 20% chance to cause 10 damage per second for some time, becomes a 100-damage attack with a 25.8% (0.20 * 1.29) chance of causing 12.9 damage per second.

The wording of many things in Borderlands 2 can be inconsistent at times. The exact distinction between shock vs. electrocute, burn vs. fire, etc., can be rather muddled in places.

Solution 2:

A post in the Gearbox Software forums stated that "Both Zapper and Catalyst [Class Mods] are all electrocute damage and do NOTHING for your shock damage aside from WDT [Wires Don' t Talk] +4/5/6".

I decided to test this, and lo and behold, the Zapper's class mod description is indeed a big fat phony. Aside from the Wires Don't Talk skill bonus, it does NOT increase your direct hit shock damage at all.

To test this, I respec'ed and did not assign my skill points (to avoid triggering the Zapper Class Mod's skill points bonuses, especially Wires Don't Talk and just test its non-skill points bonus effects). I removed my shield and relics too, and armed myself with a shock Avenger.

Without the Wired Zapper Class Mod:

With the Wired Zapper Class Mod:

Notice that the direct hit shock damage is exactly the same, i.e. shock damage did NOT increase. I also tested the DoT Electrocute damage, and it seems that its damage does increase:
Without the Wired Zapper Class Mod | With the Wired Zapper Class Mod

Based on that, the correct description of the (level 61) Zapper Class mod should be:

Electrocute Damage +29%
Chance to Electrocute +29%

Also, if you're looking to increase the total DPS of a Mechromancer speccing into Little Big Trouble skill tree, I would recommend the Chaotic Evil Necromancer Class Mod instead of the Wired Zapper Class Mod. The Chaotic Evil Necromancer Class Mod also gives a bonus to Wires Don't Talk while increasing your fire rate and critical hit damage (actually works).