It just doesn't make any sense ILO figures allow for international comparisons but you need to include the labor force participation rate into the comparison so you know what percentage of the total population is used for the unemployment and employment statistics. In the case of adults in labor markets that are mostly based on the formal sector the labor force participation rate (that is the number of people who are looking for work or currently employed) is usually pretty high but in the case of youth or in countries with large informal sectors or subsistence farming sectors it's key to doing any analysis of unemployment/employment data.
More seriously, if this is the standard of knowledge possessed by a senior economic journalist on one of the serious papers I absolutely despair. It took me a few moments to check the definitions on the ILO site. I'm not a domain expert, but I can read.
However, I'll admit that I may be biased since I work on unemployment issues and that economic correspondents have plenty of other economic related items to keep in their heads. Nevertheless, as you point out, the ILO does give fairly clear definitions of how it's measures are calculated.
I've complained about Ashley Seager in the past, and again on the article you link to, Alexandra. The whole thing is appalling. Yet Seager's response to Ted Welch (see above) shows he does not care.
