I wasn't completely surprised--or, actually, I was surprised that the script and director kept the bromance, not surprised that it was there.
The Eagle is based on Rosemary Sutcliff's book, The Eagle of the Ninth, and Rosemary Sutcliff unapologetically presents male-male close companions in her works. Book Marcus and Esca are on the same wavelength from the moment they meet until they become very nearly the other's second self. The female romantic character (Marcus's match) is a decent, strong character but one gets the impression that Esca will remain the most important person to Marcus for the rest of his life.
Like with Wings, it is difficult not to perceive a homoerotic element. It helps to realize the Sutcliff was writing in the 1950s when such relationships (still) did not automatically get interpreted as including sexual tension. Men were allowed to have buddies. Salacious rumors attached to people like Hoover for entirely political reasons.
In addition, Sutcliff's father was a Royal Naval commander, and she spent a great deal of time in military ports and around military men. She would definitely have related to Shakespeare's "band of brothers--we few, we happy few."
The movie allows for the strong pull between the men though it does change the order of events. In the book, Marcus frees Esca before their quest beyond Hadrian's Wall, not at the end. And he never doesn't trust him. The growth in the movie from distrust to friendship makes sense for a film and is well paid-off.
What impressed me most was that despite adding in the tension, the scriptwriters gave the characters the same all-encompassing bond as in the book.
When Esca comes for Marcus so they can make their escape with the eagle, Marcus states not, "Why did you betray me?" or "I thought you'd betrayed me" or, even, "It's about time" but, instead, "I thought I'd lost you."
I have written more about The Eagle, movie and book, on Votaries. I will state here, again, that it impresses me when scriptwriters appear to care about a book enough to preserve its vision, including its roadmap for its characters.