Challenge:
Can someone find me what in the state language refers to "modern muzzleloaders" any different than the same definition of "antique firearms"?
I think 594 took the existing language for antique firearm, which I BELIEVE is what currently covers muzzleloaders in our state today. Can someone find me something different in current wa code? If that is the case, then 594 would not apply to muzzleloaders.
I do not think 594 fundamentally changed the definition of a muzzleloader compared to how the state listed it before. All I can find in the WAC is reference to antique firearms, for which muzzleloaders count as a "modern replica". 
You are correct, I-594 did not change the wording of RCW 9.41.010:
(1) "Antique firearm" means a firearm or replica of a firearm not designed or redesigned for using rim fire or conventional center fire ignition with fixed ammunition and manufactured in or before 1898, including any matchlock, flintlock, percussion cap, or similar type of ignition system and also any firearm using fixed ammunition manufactured in or before 1898, for which ammunition is no longer manufactured in the United States and is not readily available in the ordinary channels of commercial trade.
To distill that, (1) means all muzzleloaders (non-centerfire, non-rimfire, subject to AG opinion point below) such as "including any matchlock, flintlock, percussion cap, or similar type of ignition system" AND any centerfire/rimfire pre-1898, subject to the commercially available ammo provision.
HOWEVER, RCW 9.41.010 does allow that "[ u]nless the context clearly requires otherwise, the definitions in this section apply throughout this chapter."
That is, context of I-594 can change the definition of "Antique firearm." Does it?
(9) "Firearm" means a weapon or device from which a projectile or projectiles may be fired by an explosive such as gunpowder.
Not changed by I-594
(25) "Transfer" means the intended delivery of a firearm to another person without consideration of payment or promise of payment including, but not limited to, gifts and loans.
Changed/Added by I-594, but uses unchanged RCW 9.41.010 definition of "Firearm."
(4) This section does not apply to:
(b) The sale or transfer of an antique firearm;
New section of I-594.
Because I-594 does not change the definition of "Antique firearm" or "Firearm" and exempts "[t]he sale or transfer of an antique firearm . . . ," I would expect that the existing state practice, for which I presume is not requiring backgrounds checks for retail sale of modern muzzleloaders, would remain the same post I-594.
However, note that the existing definition of "Antique Firearm" has that murky clause, "and manufactured in or before 1898 . . . ." I would have expected that someone has obtained an AG opinion in the past that interprets that clause as allowing sales of post-1898 muzzleloaders without background checks.
Disclaimer: don't take internet legal advice.