What you have here, I believe, is called a Group Genitive (see Collins). See the third section for more on this.
Meaning in Context:
From Cambridge, a bloke is "a man, often one who is considered to be ordinary." This is used informally. See sheila.
In your case, Harry is saying that he saw Gaunt waving (= brandishing) the ring "in the face of a Ministry official (= Bob Ogden)."
The sentence would look something like this if you simplify it:
... waving it in the man's (= man from the Ministry) face.
... waving it in the bloke's face. The bloke from the Ministry.
... waving it in the bloke-from-the-Ministry's face. [The hyphens make it easier to read this]
... waving it in the bloke from the Ministry's face.
From this EL&U post Difference between “at someone's face” vs “in someone's face” vs “to someone's face”,
"In my face" is used when someone is confronting you, arguing with you, or pointing out that they believe you have done something wrong."
Strange or not:
To me, "bloke from the Ministry's face" seems a bit strange with regards to the possessive ('s) - it is too far removed from "bloke". This might be acceptable in informal contexts (e.g., casual conversation among friends).
If "the bloke from the ministry" is being used as a nick name or a title in this context, then it could be treated like a noun.
On Group Genitive:
There are other examples that resemble the possessive (called a group genitive) in your case. See Formation of possessive construction for "the king of Spain's", "the man we saw yesterday's", and "the King of England's" (Miles provided this link in the comments).
See this ThoughtCo. article: Group Genitive
In English grammar, the group genitive is a possessive construction (such as "the man next door's cat") in which the clitic appears at the end of a noun phrase whose final word is not its head or not its only head. Also called a group possessive or phrasal possessive.
Group genitive constructions are more common in everyday speech than in formal writing.
Also see this EL&U post Adding a possessive to a singular noun phrase that ends in a plural noun for similar strange examples: "The clock under the curtain’s hour hand broke off", "The clock mounted on wheels' hour hand broke off", and "the Queen of England’s hat".
The EL&U post cites this source material: The English “Group Genitive” is a Special Clitic. I don't have the expertise to understand the technical aspect of the paper. But it does have similar expressions: "The man in the hall’s taste in wallpaper is appalling."