I think it's supposed to be a threat display, but yes. This is an escalation from the previous US doctrine not to first strike other nuclear powers.

Note that even the previous doctrine implicitly but clearly stated that the US reserved the right to do a nuclear first strike on nations that do not have nuclear weapons themselves (something which the US has done before and has considered doing again at least twice, in Korea and Vietnam). The only nuclear powers who have officially declared not to nuke first under any circumstances are India and the PRC.