Maybe the family of the child has visitors and they are showing around the house to them. Like "here's the balcony", "here's my room" etc Δείχνω means "show" but it can also mean "point to/at". For example: "δείξε μου το βιβλίο σου" means "show me your book" and "σταμάτα να δείχνεις, δεν είναι ευγενικό" means "stop pointing, it's not polite". The child here is probably showing around.
Well, I don't think anyone would come across this sentence in a newspaper to begin with, unless that balcony was something extraordinary. ;D However, I'll agree that when δείχνω means show, it's more natural for it to be followed by the object. When it means point out, like G.Georgopoulos mentioned in his comment above, it's okay.
The tiles for answering are generated automatically, at least partly from the hints -- and the hints sometimes contain not only translations but also little notes to the learner such as "acc" for "accusative case".
Those shouldn't really turn up as tiles but Duo isn't smart enough to tell them apart from the translations, unfortunately.