Obviously, you will not like this movie if you did not like 1988's Bloodsport (though there ARE some cases where the sequel is better than the original). This review is thus addressed to those who liked Bloodsport and are wondering whether they should bother to watch Bloodsport II: The Next Kumite. My answer would be yes.
Sure, Jean-Claude Van Damme isn't here (Donald Gibb serves as the link between the two movies), but Daniel Bernhardt, as petty thief Alex Cardo who discovers the meaning of honor, makes for a likable, charismatic lead, who also bears somewhat of a resemblance with Jean-Claude.
Also interesting is the narration, told in flash-back by Alex Cardo's trainer, Master Sun (played by James Hong) to a throng of young disciples. In these moments in particular, Bloodsport II shows that it is completely aware of what kind of movie it is, that it does not aspire to be anything more, and even pokes fun at itself (see the excellent ending, for example).
In short, Bloodsport II: The Next Kumite is not as awesome as it's predecessor, but it does what it aspires to do: it gets the job done. The cinematography isn't as good here as the first time, making the fights less impressive, but they're good enough. The story and the fact that the movie changes location (from Hong Kong to Thailand), contribute to not make it a rehash of the original. The actors, from Daniel Bernhardt to Donald Gibb, passing by James Hong and Pat Morita, are just right. And just like in the first one, you may know exactly how it's going to end, but it's still a joy to watch.
