From the introduction to Tullian's book:
The unintended consequence of this push [for a more radical expression of Christianity], however, is that if we're not careful, we
can give people the impression that Christianity is first and foremost
about the sacrifice we make for Jesus rather than the sacrifice Jesus
made for us; our performance for him rather than his performance for
us; our obedience for him rather than his obedience for us. The hub of
Christianity is not "do something for Jesus." The hub of
Christianity is "Jesus has done everything for you."
Our relationships, our careers, our institutions also run on the
principle of "I'll do X for you, if you do Y for me." Everything in
our world demands two-way love. Everything's conditional. If you love
me, only then will I love you. If you give to me, only then will I
serve you. This conditionality plagues us at every turn and keeps us
enslaved to fear, reservation, and insecurity.
Thus, "one-way love" means unconditional love. Love that doesn't demand reciprocity. Their aim is to show the unconditionality of God's grace.
In the video at your link, Elyse Fitzpatrick says:
You don't have to worry anymore about whether or not you're loved. You're loved, so you can love now because you've been loved.
This could almost itself be a paraphrase of 1 John 4:19. The idea, however, as Caleb said in the comments, is that "the instigator in the equation was God and his love and we only reciprocate because he initiated."
Here are some more comments from Tullian Tchividjian about 1 John 4:19: