Connect to API in Power Query - Error: Block length does not match with its complement.

Even if the error is the same, this is a slightly different problem: the links on this page actually return zip files, and what's more the zip files themselves contain multiple files. You should use the API to return the data in directly, for example in JSON format, as described in the section "Output format" here. Here's a quick example:

let
    Source = Json.Document(Web.Contents("http://api.worldbank.org/v2/country/all/indicator/SP.POP.TOTL?format=json")),
    #"Converted to Table" = Table.FromList(Source, Splitter.SplitByNothing(), null, null, ExtraValues.Error),
    #"Changed Type" = Table.TransformColumnTypes(#"Converted to Table",{{"Column1", type any}}),
    Column1 = #"Changed Type"{1}[Column1],
    #"Converted to Table1" = Table.FromList(Column1, Splitter.SplitByNothing(), null, null, ExtraValues.Error),
    #"Expanded Column1" = Table.ExpandRecordColumn(#"Converted to Table1", "Column1", {"indicator", "country", "countryiso3code", "date", "value", "unit", "obs_status", "decimal"}, {"Column1.indicator", "Column1.country", "Column1.countryiso3code", "Column1.date", "Column1.value", "Column1.unit", "Column1.obs_status", "Column1.decimal"}),
    #"Expanded Column1.country" = Table.ExpandRecordColumn(#"Expanded Column1", "Column1.country", {"id", "value"}, {"Column1.country.id", "Column1.country.value"}),
    #"Expanded Column1.indicator" = Table.ExpandRecordColumn(#"Expanded Column1.country", "Column1.indicator", {"id", "value"}, {"Column1.indicator.id", "Column1.indicator.value"})
in
    #"Expanded Column1.indicator"