Don’t want to belittle the achievement but they launched it as in „had it launched by the commercial launch provider SpaceX“, not on a self-developed rocket as it sounds like on the first read.
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Edit (rather than reply and make the comment chain long): It's fine that you read it that way. I figure that if the article were about a launch vehicle then it would have been the rocket's name in the title, and if the article were about the satellite then it would have the satellite's name (BOTSAT-1). If Botswana had developed both an orbital launch vehicle and their first satellite then I'd bet the headline would have been sensational.
It’s more a case of does it make economic or strategic sense to do so. For most countries it wouldn’t.
Sure, developing a single satellite isn't something that makes a lot of sense in a first order economic assessment. They are definitely not going to be able to sell the data they collect for the millions of dollars they spent on the program. And they definitely spent more on the satellite than they would have spent buying equivalent imagery from commercial providers for the next few years. There is almost no chance that they will have a satellite with competitive technical specs.
But nobody is comparing Botswana to NZ. This is their first satellite. Having a satellite program at the national university is a point of national pride. It will inspire their young people and encourage them to study STEM. It gives valuable practical experience to their people, some of whom might go on to start a space systems company and bring high tech business opportunities to their country. This is a step toward moving part of their economy from being based on natural resources (diamonds, the value of which are subject to the whims of a cartel that they don't control), to being based on knowledge.