Gunnarsson will re-enter the draft. Europeans need to either be drafted twice and not sign in order to become a UFA or hit age 22 without ever being drafted.
As Gunnarsson was drafted at age 20, he still has to get drafted again in order to become a UFA.
Not sure where you're getting the "need to be drafted twice" bit. but this is straight from the new cba -
20
ARTICLE 8 8.6-8.6
Notwithstanding any provision of Sections 8.6(a) or (b) to the contrary, if
a Player drafted at age 20 or older is drafted from a club outside North
America, his drafting Club shall retain the exclusive right of negotiation
for his services through and including the second June 1 following his
selection in the Entry Draft. The Club need not make a Bona Fide Offer to
such Player to retain such rights.
(iii) Upon the expiration of the applicable exclusive right of negotiation as
outlined in subsections (i) and (ii) above, the Player shall be a draft-related
Unrestricted Free Agent.