the obvious: Portugal's pink map wank gets a major boost. Basically the entire southern Africa situation changes dramatically.
the maybe not so obvious: I believe Rhodes was one of the big drivers of DeBeers, so maybe without him, you could actually afford a diamond for your gal's finger.
He was big in the Jameson raid, and it sparked Kaiser Bill 2's incendiary letter. So maybe you have better German/English relations.
Without the Boer Wars to befuddle Britain, maybe they don't re-org their military, leading to problems down the road in a little dust-up called the Great War.
Without the Boer Wars to occupy Britain, maybe the Venezuala Crisis dusts up bigger (OTL Britain basically backed off and let the US puff up their chest because Britain was busy elsewhere).