This is not a mistake and it is perfectly fine to use such expression even in the modern days (it is more common to see it in formal writing though). In short, there is nothing wrong with having a verb in gerund form be used after a possessive determiner.
Gerunds preceded by a genitive
Because of its noun properties, the genitive (possessive) case is
preferred for a noun or pronoun preceding a gerund, which is
functioning as the subject of the gerund's verbal element.
We enjoyed their [genitive] singing.
This use is preferred in formal writing or speaking. In casual speech,
the objective case is sometimes used in place of the possessive:
I do not see it making any difference. (I do not see its making any
difference is correct.)
Using the possessive case with the gerund is applicable in all
situations. For instance:
He affected my going there.
He affected your going there.
He affected his/her/its going there.
He affected our going there.
He affected their going there.
He affected Mary's going there.
The verbal action of the gerund belongs, in effect, to the subject
practising it; thus, the possessive is required to clearly demonstrate
In some situations, either the possessive or the nominative case may
be logical, but with slightly different meanings; but when the
nominative case is used the verbal element is a participle, not a
The teacher's shouting startled the student. (Shouting is a gerund,
and teacher's is a possessive noun indicating whose shouting is being
talked about; but shouting is the subject of the sentence.)
The teacher shouting startled the student. (Shouting is a participle
describing the teacher. This sentence means The teacher who was
shouting startled the student. In this sentence, the subject is the
teacher herself. A clearer way to write this sentence might be The
teacher, shouting, startled the student.) Either of these sentences
means that the student was startled because the teacher was shouting,
but the first places greater emphasis on the shouting by making it the
subject of the sentence, while the second places greater emphasis on
the teacher and is not using a gerund.
Despite such examples of a similar construction that uses a participle
instead of a gerund, using a noun or pronoun in anything except the
possessive case as the subject of a gerund (He affected me going
there) is incorrect in formal writing.
However, the usual accusative is a less formal alternant. In a few
situations, the genitive becomes redundant. For instance,
He objected to the girl being appointed the President. (Alternatively,
He objected to the girl's being appointed the President.) We were
delighted at Paul being awarded the prize. There is no chance of the
snow falling. (Not, There is no chance of the snow's falling.)