All those have a higher percentage of Christians in their populations than the US or anywhere in Western Europe, and they don't have the same level of anti-terrorism focus so are presumably easier targets.
Could it simply be that those countries haven't been bombing and invading places in the Middle East?
These countries have negligible numbers of Muslims.
There have been multiple Islamic terrorist attacks in Tanzania (which borders Zambia) and Kenya, both of which have significant Muslim minorities. Not to mention the frequent attacks by Boko Haram et al in Nigeria and the perpetual civil war in Somalia, which is overwhelmingly Muslim.
Even the threats and attacks against cartoonists, as mentioned by another commenter, go beyond the simplistic "kill all infidels just because they exist".
To put it more simply: when Danish cartoonists are threatened for offending Islam, is that also because of imperialism?
And why would you believe them? What they say on TV is also a weapon. People who don't come and negotiate but go straight to killing won't be posting their real goals on their website, they'll rather post something that helps further those goals.