The intro works fine for a game because it's immersive. But directly translate that onto the screen and you have a series of exposition dump conversations that have little to nothing to do with the plot. You just can't do it that way and expect the audience to keep up (see:'Golden Compass'
Also keep in mind that the game slowly immerses you in the word, drip feeding background information here and there and even provides a whole codex of information for further details. A movie doesn't have the luxury of time to do it that way (nor of course is the codex an option.
Actually, let's take a look for ourselves: -
So we go from an out of context conversation about Shepard, to a text crawl, to a nice building musically supported crescendo showing off the Normandy and out main character which, to be fair you probably just spent upwards of 5 minutes creating (not so if this were a movie.)
Next, after Nihlus's introduction it's established that he's not part of the crew but an observer from something called the council. There is implicit distrust regarding this arrangement. Then we get a conversation about how mysterious our assignment is. Spectres are mentioned twice.
After a brief audio only introduction to Anderson, we're told to meet him down in the comm room. What follows are two optional conversations (I actually had a hard time finding a video clip that actually includes them!) that tells us about Turians, the First Contact War, Spectres, Normandy's function as a stealth ship, Spectres, some vague background about Anderson, more paranoia about the mission, Spectres, the council, Spectres, Shepard's background, Spectres, C-Sec, Spectres, Spectres, Spec--seriously, you could make a drinking game out of how often Spectres are mention in the first 10 minutes!
So yeah, we haven't even gotten to the comm room yet and already we're half way up to speed on the ME universe. Speaking of which, our conversation with first Nihlus then Anderson covers Eden Prime, humanity's rapid expansion, the fact their newcomers to the galaxy and the true nature of our mission (that mystery lasted all of 3 minutes!) Then things really ramp up and we're told about protheans their technology & sudden mysterious extinction, mass relays, the citadel, the beacon, the Mars archive, the attican traverse, the terminus systems...oh and hey, spectres!
Cut to plot twist #1 and our first glimpse of a reaper then we're off to Eden Prime....
Now don't get me wrong, it's a good intro that sets the tone very well and introduces the main character as well as Joker & Alenko, capturing their nascent personalities quite well. However, half it's purpose is to intoduce the player to the conversation wheel and movement controls (BTW, I really wish ME3 had done this.) As and interactive experience a game player is more inclined to go at their own pace as they get to grips with everything around them. Try doing this in a movie and all you'll get is a bunch of talking heads and a very bored audience.