Learn English – What does “Way to read the room” mean

As Dan Bron points out in a comment above, "reading a room" refers to quickly taking in a room's prominent features—including, perhaps, the mood, biases, and tendencies of its occupants—in order to make an informed decision about how to make the best possible impression in it or (perhaps) to achieve maximum profit from it.

As this description suggests, the term gained relatively early prominence in marketing and management guides, such as G. R. Ambrosius, The Art of the Possible (1991) [combined snippets]:

The moderator is able to "read" the room on many dimensions. These include:

• seeing the room as a group of strangers vying for the approval of the moderator and new "peers."

• noting that individuals within a group have a behavior range that runs the gamut from dominant to withdrawn.

• seeing when a participant wants to speak before a hand is raised, and "reading" non-verbal clues appropriately.

But the earliest Google Books search match for "read the room" is a book on theft and other types of opportunistic criminality. From Israel Drapkin & Emilio Viano, Exploiters and Exploited: The Dynamics of Victimization (1974) [snippet]:

In dealing with offenses involving theft of and from purses, when purses were uppermost in my mind, I began to look at and to look for purses on the street, in stores, in restaurants, in cinemas and was astonished to see just how many purses there were and just how careless some women were with their purses in what they did with them. I learned that one can enter a room and read the room in terms of purses.

The sarcastic comment cited in the OP's question—"Way to read the room!"—is (again as Dan Bron points out) structured similarly to something a sarcastic sports heckler might say in mock approval after seeing a player drop a potential touchdown pass in a (U.S.) football game: "Way to blow an easy six points!" where "Way to..." is a short-form way to express the idea "That's the way to..."

The implication in the cited movie script is that the "Friend" who expresses satisfaction about killing the patient has seriously misread the prevailing sentiment in the room toward the patient and toward the prospect of saving or killing him.

Because the expression is idiomatic, a literal translation might prove baffling to audiences reading it. But sarcasm is difficult to translate even when idioms aren't an issue. Perhaps the safest way to render the scene is by making the Doctor's reaction to the Friend's comment unmistakable:

Doctor: Find something sharp to penetrate his skull. [to help the patient.]

Friend: About time we killed him.

Doctor: Your humanitarian instincts once again leave me in awe.

or:

Doctor: Find something sharp to penetrate his skull. [to help the patient.]

Friend: About time we killed him.

Doctor: You may be the only person in the room who feels that way.

or:

Doctor: Find something sharp to penetrate his skull. [to help the patient.]

Friend: About time we killed him.

Doctor: Have you been reading "How to Lose Friends and Antagonize People" again?