I read the last phrase (omitting the « tous/tout » issue):
« … comme ceux des pays voisins que sont le Mali et le Niger. »
« … just as [the presidents] of neighboring countries, Mali and Niger [have done]. »;
whereas you appear to read it to mean:
« … just as [the presidents] of countries neighboring Mali and Niger [have done]. »
If you are in fact reading it to mean the latter, then try reading it to mean the former to see if it makes more sense.
The « QUE sont le Mali et le Niger » construction perplexes me (and maybe you, too) because I always thought that 'QUI' takes a verb, whereas 'QUE' takes a subject, but maybe the subject/verb have been inverted here:
« ... QUE le Mali et le Niger sont (voisins des 4 autres pays cités) » to express that Mali and Niger are two AMONG SEVERAL countries that neighbor the other 4 countries mentioned, but not the only 2 (which perhaps « QUI sont le Mali et le Niger » might imply). (or maybe « que sont » is just an idiomatic usage that I don't recognize)
Anyway, I see that what I had intended to be a 'comment' is much too long to fit anywhere else than here as an 'answer,' but I’ll go ahead and post it anyway in hopes that it helps a little (at least to show that you weren't alone in finding this confusing).