Analyzing this it seems to be counting the number of different
chemical element symbols consecutively contained in the word.
China has three more than Chile
We may compare by looking at the last three letters:
ina has Iodine (I), Indium (In), Nitrogen (N) and Sodium (Na), while ile has only Iodine (I).
Algeria has one less than Nigeria
Then the first three letters:
Alg has only Aluminium (Al), while Nig has Nitrogen (N) and Nickel (Ni) - we don't count Iodine (I) again as Nigeria already has it.
Ireland and Iceland...? Are they even different?
The first three letters:
Ire has Iodine (I), Iridium (Ir) and Rhenium (Re), while Ice has Iodine (I), Carbon (C) and Cerium (Ce).
Hence Ireland = Iceland which is fair and elementary :P
HINT:The numbers are only correct as of this writing, they might change in the future (though unlikely)
New elements are discovered and named, but it's unlikely they would have symbols contained in the bolded letters.