I talk about spiritual love in the article linked below. The kind of love that makes the most sense in existentialism, I think, is camaraderie or teamwork in a common rebellion (against nature as the absurd and amoral wilderness). Pity and compassion are also compatible with the tragic aspect of existentialism.
In any case, no I don't think existentialism entails the rejection of all kinds of love. But in the West, the word "love" has been tainted by two millennia of Christianity and more recently by some New Age "spiritual" charlatans.