Probably not during ML as it is not "loaded from the muzzle" by the definition of ML, also any legal gun with more than one barrel can only be loaded with one round.
I also see that it says ML handguns must have a barrel at least 8 inches long and use 45 grain equivalents of black powder. This in the Equipment and Hunting Methods section of the regs. Your's meets the barrel length but I'm pretty sure it won't even fit 45 grains into it.
So, nope, not legal during muzzleloader season.
They may be used for forest grouse, rabbits, and hares.