Solution 1 (Accepted):

The problem is the NA values in y. After you go to long format, you can simply omit them:

plot_data = DF1 %>%
  na.omit %>%  ## add this here
  group_by(variable) %>%
  arrange(value) %>%
  mutate(xcoord = seq(-0.25, 0.25, length.out = n()))

ggplot(plot_data, aes(x = variable, y = value, group = variable)) +
  geom_boxplot() +
  geom_point(aes(x = xcoord + as.integer(variable)))

enter image description here