No lawyer here but i'd "guess" they have a case...
Recommendation: Comply with all they're asking for.
As for the amicably, i think it means two things here:
1) From what you have posted, it seems they don't even ask you to turn the domains to them.That indeed would be amicably.
2) It probably also means, so far it has been amicably and they don't want you to go bancrupt but they have non-amicably ways too if you should choose to not comply.
That's how i would interpret this.
Do *not* interpret amicably as "We want to *buy* your names" though.