Is it simply that you're less used to reading short stories than novels -- short stories typically leave far more unsaid, even though this is an extended one, comparatively speaking?
I don't think it's necessary to know anything about the history of Cambodia, other than what the story tells us, which is that it has had a genocide, and is poor enough for its embassy to not be with the other London embassies, somewhere rather grander in central London, but in a suburban house in Willesden, on a street with vulgar mansions, convents and retirement homes.
Fatou is fascinated by it, partly because of its oddity, of the apparently eternal game of badminton going on in the grounds, with the players invisible, just the shuttlecock visible over the fence, partly because of the young white people going inside, presumably for travel visas to visit Cambodia, a developing country, as tourists, while Fatou herself has travelled from Ivory Coast to Libya to Italy to London not as a tourist but as an economic migrant working menial jobs, paid for by her father (it's not clear whether he, or some people smugglers, or anyone, are benefiting from her enslavement by the Derawals, and nor is it clear how she got to the UK...)
Also fascinated by the Embassy is the nameless elderly woman standing on the balcony of the old people's home across from it, and who narrates the non-Fatou parts of the story, who is a sort of personification of Willesden, which is a melting pot of immigrants -- the Cambodians, Fatou, her Nigerian friend Andrew who has converted her to Catholicism, whoever lives in the houses with the names in Arabic, the awful (possibly Pakistani?) Derawals, who run a chain of suburban grocery shops and whose children have London accents. Andrew is kind, though misinformed and condescending, but other immigrants are not always allies.
Fatou is also fascinated by it because she has so few things to think about other than her own past as an immigrant in different countries, her rape, her conversion to Catholicism (she's fascinated by water in all her different contexts, whether it's baptism or swimming) -- she has no phone, no internet access, no TV, and only gleans scraps of news from discarded newspapers. In a Metro, she has read about a slave, but thinks she isn't one, because she's allowed out to go shopping (though she has no access to her passport, and is unpaid. The family fire her after she saves their ten year old from choking, and don't want to have to feel grateful, or treat her like a human being. (It's fairly clear that no relative is going to be staying in Fatou's tiny room...) Her only source of help is Andrew, who says he won't tale advantage of her sexually and will find her a job as a cleaner in the offices where he is a security guard. The story ends with her waiting for him outside the Embassy, watching the shuttlecocl appear and disappear behind the wall.