A clumsy attempt at reproduction:

library(maps)
library(sf)
library(ggplot2)

world1 <- sf::st_as_sf(map('world', plot = FALSE, fill = TRUE)) |>
  st_transform(crs = 4326)

ggplot() +
  geom_sf(data = world1) +
  scale_y_continuous(breaks = seq(20, 90, by = 10), labels = NULL) +
  scale_x_continuous(breaks = seq(-120, 180, by = 60), labels = NULL) +
  labs(x = NULL, y = NULL) +
  theme(
    panel.background = element_blank(),
    panel.grid.major = element_line(
      linewidth = 0.25,
      linetype = 'dashed',
      colour = "black"
    ),
    axis.ticks = element_blank(),
    axis.text = element_blank()
  ) +
  labs(caption = "Designed by Mikey Harper") +
  annotate(geom = 'text', x = I(0.5), y = I(0), label = '0°', vjust = 1) +
  annotate(geom = 'text', x = I(0.97), y = I(0.77), label = "120°E") +
  annotate(geom = 'text', x = I(0.97), y = I(0.25), label = "60°E") +
  annotate(geom = 'text', x = I(0.02), y = I(0.77), label = "120°W") +
  annotate(geom = 'text', x = I(0.02), y = I(0.25), label = "60°W") +
  annotate(geom = 'text', x = I(0.5), y = I(1), label = "180°W", vjust = 0.4) +
  annotate(geom = 'text', x = I(0.5), y = I(0.6), label = "80°N", vjust = 0) +
  annotate(geom = 'text', x = I(0.5), y = I(0.76), label = "60°N", vjust = 0) +
  annotate(geom = 'text', x = I(0.5), y = I(0.9), label = "40°N", vjust = 0) +
  coord_sf(
    crs = "+proj= ortho +lat_0=90 +lon_0=0",
    expand = FALSE,
    clip = FALSE
  )