On Doom, Lotor isn't exactly planning on sending any Doomite representatives to the Games. Rather, what he plans to send is a special Neuro Robeast that can infect a machine and take it over (it wouldn't due to infect Voltron, explains Haggar, as he'd easily override the beast). They decide to target the earth mover and so deliver their little troublemaker in the dead of night. The little village boy wakes up and witnesses this, but when he wakes the VF they think he was dreaming. That is, until the machine acts on its own.
Pidge gets into the passenger compartment and manages to stop the machine before it totally destroys the stadium. While he and Hunk look over its circuitry, the children have a seat inside the machine. One of the kids inadvertantly turns the machine back on which allows the robeast to take control again - the kids are strapped into their seats against their will while the machine goes off on another destructive rampage.
The Princess realizes what is going on from the Castle and heads out in her Lion to help. But Lotor clues her in on the hostages within the machine - the kids - so she's limited on what she can do. So she floods the area with water. It works, shorting out the robeasts' hold over the machine, frees the kids from their seats and affords them a way out via a busted windshield. But since Allura almost drown the VF with the water, she's busy rescuing them. That unfortunately gave Lotor and the robeast time to recover, seal the windshield and keep their hostages.
The boys get to their Lions, and Hunk goes on foot to rescue the kids. He succeeds, which infuriates Lotor. To retaliate, he has the machine morph into a Robeast. Voltron is formed and in perhaps one of the quickest battles yet, dispatches the rogue machine.
Now the problem is, how to rebuild the stadium now that the earth mover is destroyed? The answer is use the Lions, of course. The stadium is rebuilt in time and the games go on.