Sounds like a bug to me: Anya and Guy should leave if the Main attacks Somnus.
Either way, I'd expect the slave bracelet to work on all sentient beings (with possible excpetion of the spirits) and I definitely wouldn't be surprised if they were used on Spriggats. Drawing from info on TPA2, Shadowlings can be slaves, and I guess the way to control them would be through slave bracelets (and same argument goes for the Spriggats). As for Gamblin' Jack, it seems that the Main has the option of setting him free or keeping him as a slave (hence, I'd suspect, as Ert points out above, that the Main might be able to use the slave bracelets- it's just simple transfer of owner rights, and given the way it communicates with the owner, like Tastidian punishing the Main if he fought Flavin, methinks a Psy owner is one of the limitations- otherwise how will the owner properly control/punish the slave and set the "rules" for the bracelet to force onto the slave?). Either way can explain why Gamblin' Jack remains with the Main even if the Main sides with Tastidian: eg he might feel that he owes the Main his freedom and will not question the Main's actions, unlike Anya and Guy (or Grotius, for that matter- he doesn't desert the Main, although the Psy Academy did side with Spriggats). And Helena keeps on as a mercenary, even though she is helping the Main to subdue the humans... Thus, it's not too surprising that Gamblin' Jack would stay in that case.
