Most importantly, it tells you that they think those characteristics are important or impressive (although perhaps only indirectly, in that they think you think they're important for this role). You might be able to conclude more from the fact that someone thinks loyalty is worth mentioning here, than you can from their belief (or claim) that they're loyal!
It doesn't tell you that they actually possess the characteristics to any remarkable degree. Especially something completely vague like "out-of-the-box thinking". You might read that and figure that all of your candidates think out of the box, not just this one, but some of them would call it "having a good idea".
As for whether there's any merit in it -- if its a CV posted online, then it makes a lot of sense to have some kind of summary up top indicating what kind of jobs you're looking for, why you want them, and what basic attitude you bring. This kind of "personal qualities" stuff often creeps in there. If it's a CV submitted for a particular application with a cover letter, then it probably repeats stuff from the cover letter, although it might still be a worthwhile summary of why they're good for the role. You could view it as a reading comprehension test, "has the candidate accurately identified and summarized what the role calls for?".
Ideally it's backed up by relevant experience, in which case it serves as a sort of abstract of the result the author wishes to prove in this paper, but that's not always practical. If you believe yourself to be unusually loyal it might be quite easy to present examples of this, but quite difficult to put those examples in your CV, which operates well above the level of specific incidents in which you demonstrated loyalty. Therefore this statement in the CV is (intentionally or otherwise) bait. It might induce you to ask at interview a question that the candidate has (you'd think) prepared for. Of course, if you cared about loyalty then you'd be asking all candidates about loyalty, and if you don't care about loyalty why waste interview time drawing a rehearsed answer? So you can argue it's complete pointless as far as that goes, except that I suspect in practice it does occasionally prompt an interviewer to talk about something they otherwise wouldn't, just like the also-controversial "hobbies" section.
It would seem to me irrational to ignore this information in a CV, if you would pay attention to exactly the same thing written in a cover letter (I'm not sure if you're saying you actually do that not). Unless you're extremely busy and have clear instructions written in whatever process they went through to submit the application, it's pretty much nonsense to punish applicants because they don't follow your conventions of what goes where.