I wonder how Larousse got the idea. "Sich widmen" can both refer to small things (a newspaper, a stamp collection, etc., for a short time, but being absorbed by them) and to a mission in life (which takes up all your energy). It is slightly elevated in style (especially "etwas etwas widmen", the first 2 ex. above) but can also be used ironically such as in: "Während sie nicht aufhörte, ihn mit Vorwürfen zu überziehen, widmete er sich eingehend dem Muster seiner Krawatte."
It is rarely used in spoken speech, as far as my memory goes, but you can readily hear sentences such as "Du könntest ruhig den Kindern mehr Zeit widmen!"
"Sich befassen mit" is a more neutral expression and may also be more prevalent in spoken German, but this expression lacks the dimension of, erm, eh, well, dedication which "widmen" has.