Your posts always make me chuckle. Your smug insistence that you're the worldly one compared to us insular Brits always ends up tripping you up. Here you are showing your ignorance about baseball's popularity, purely because it isn't played on your own doorstep. I like handball but baseball is far more widespread and played in bigger countries than handball.Basketball is very likely the number two yes.
Handball, volleyball and rugby are also up there in some widespreadness.
Obviously handball is very eurocentric. It is big in Europe, bigger than most in UK will imagine:
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But there's also decent teams from North Africa, Asia and South America, while Australia is a nice punching bag in every tournament.
The strongest challenger against basketball as the second most popular sport is probably volleyball, which is very popular (don't think I've personally watched a game but that doesn't matter) across the world and where every continent seem to be competitive at the international stage.
Cricket and baseball, in terms of widespreadness, are of course rather small sports - they're just popular in a couple of big/loud countries.