That would be very wrong.
It would be a very flawed approach if google responded to searches made on Google.ng by returning only results on sites hosted on .ngs and .com.ngs. Very flawed.
To further detail on why the likes of .fi carry SEO weight locally, you need to also understand that all Google.fi competing sites are not in English but in Finnish. Once an English word appears on a webpage that webpage automatically is a competitor for the word or phrase across all English webpages - which numbers in their bullions.
And that dilutes what it should specifically be ranking for, until the weight of that is aggregated across the other pages and the site as a whole; which will carry localized strings like a local name or area, this is why using '....In Nigeria' / 'in Lagos' would immediately redefine your search and get you what you're looking for. So in essence our local sites are also competing globally across all English written sites because they are in English, that is why you'd little locality when you use .ng google extension to search and why you'd need to further filter by adding 'in Lagos' / 'in Nigeria' string.
Another very important thing you need to also know is that Google is not particularly interested in what going on in Nigeria's search results - what's happening on Google.ng is not of major importance on the scale of things. How much does that extension bring them yearly compared to others? Who are our biggest ad spenders and how much do they spend? Compared to other markets, na pocket change. Google is prolly still running outdated search algo on that .ng google extension. -#jk