And actually, come to think of it, the Paradox Brothers never used it anyway, so your point is incorrect. (Having it in Duel Links isn't an indication they've used it in the anime or manga. ;p)
The indication is that he's literally a gate keeper and probably guards a labyrinth gate. We can assume everything that has to do with labyrinths can be considered Paradox related.
...That's like saying Labyrinth Tank is Bandit Keith-related because it's a Machine. Yes, there's a thematic reason the Paradox Brothers have Gatekeeper here, but it's not even related to Bandit Keith's use of it.
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