Yes, often (not always!) befingern is used with a sexual connotation.
In your example, the subject is ein geiler Lüstling -which is something like "a horny debauchee". This leaves no doubt about the sexual connotation in this case.
And yes, if it isn't used in a sexual way, "to touch" can be an option for translation.
The Duden entry for befingern describes the meaning as:
etwas [ungeniert] mit den Fingern berühren, betasten, um es zu untersuchen
i.e. something along:
to [unabashedly] touch something with the fingers, to feel something for investigation
Examples from the same entry are:
die schmerzende Nase befingern
prüfend eine Wurst befingern
musst du denn alles befingern?
All of them can be used in a non-sexual way - although one could make up ambiguous statements using the second and third.
User scienceponder provided another non-sexual example (thank you!):
Mit seinen fettigen Händen hat er die Glasscheibe befingert.