I'm not sure I quite agree with that. As I see it, the term "luck" is regularly applied to two categories of events. As you've said, there are the chance events (such as winning the lottery or rolling a 6 on a die), and in that I quite agree with you.
The other case, which is what I thought the article was about, is more of an "opportunity" type of luck. For example, if you happened to find a £10 note while walking home. That would be called "lucky" but it is not simply the result of chance: it is the result of you being more observant than everyone who didn't notice the money before you. And in that sense, people can easily be "luckier" than others, as the article describes.
The other case, which is what I thought the article was about, is more of an "opportunity" type of luck. For example, if you happened to find a £10 note while walking home. That would be called "lucky" but it is not simply the result of chance: it is the result of you being more observant than everyone who didn't notice the money before you. And in that sense, people can easily be "luckier" than others, as the article describes.