Basically, it delivers very short pulses (microsecond region) of relatively high voltage to the battery (as much as 50 volts, depending on battery condition). Lead sulfate is a very poor conductor, but with a high enough voltage, you can force a tiny bit of current through it. Each little bit of current drives some of the sulfate ion back into solution (converting it slowly back to lead oxide).
I'm less clear on how the short pulses interact with the areas that aren't sulfated; but apparently they somehow keep the electrolyte from being split into hydrogen and oxygen (as would normally happen with a high charging voltage). I don't know if the very low duty cycle gives the ions time to recombine, or whether it just drives that part of the cell into the region known as "surface charge" without actually causing electrolysis. I do know from my own experiments (long ago), that it's important to limit the average current to a very low value, so the battery doesn't get hot or outgas. AGM batteries in particular (which is what I used to play with) will be ruined if they get hot or any gas escapes.
Back in the early 80s, I worked for a company that sold systems based on HP minicomputers that had battery backup for the solid state RAM. The backup was intended to allow them to survive short power outages without losing the program in RAM. (If the program was lost, it would have to be reloaded from either paper or magnetic tape, a rather tedious process. No hard drive.) Unfortunately, although the backup power supply would shut down if the battery got too low, it still monitored battery voltage and would eventually run the battery flat. If power was not restored in a timely manner, the batteries would be "ruined", meaning they wouldn't take a charge from a normal charger. So we got a fairly steady flow of battery packs back from the field, which the company just pitched and replaced with new. I used to salvage the packs from the trash and drag them home, where I would connect them to a bench power supply and run the voltage up until they would take just a tiny bit (20ma seemed to be about ideal) of charging current, then leave them that way for several days (or weeks). They didn't all come back, but I'd guess maybe 2/3 of them did, giving me some cool little batteries to play with.
Gates X cells were somewhat larger than a D cell, rated 2 volts & 5000 maH. One of the neat things (to an inveterate tinkerer like me) was that they could deliver a LOT of current for a short time, upwards of 50 amps when new. They worked really well for things like lighting rocket motors and starting fires.