The issue isn't necessarily shooting, in my view. It's the creeping advance of militarism into games.
"Projectiles have been part of gaming since forever," he says, and it's true – early arcades were all about shooting galleries. Think of old-school duels and kids playing cops and robbers; weapons have, in fact, been part of play for a long time. "When you get into the first-person view, shooting continues to be what feels most natural," he says.
If you look at the evolution of first-person shooters specifically, they've been violent, yes, but the focus has changed dramatically. In Wolfenstein and Doom, the main character was nominally in the military, but in the game world, they were totally cut off from their nation and command structure. Duke Nukem was an unattached action hero stereotype, while Half-Life's Gordon Freeman had a Ph.D. in theoretical physics (and a M.S. in KICKING ASS). These characters, whether they were in the military or not, fulfilled the role of the Lone Hero Winning Against Impossible Odds.
Starting in the late 1990's, most notably with Tom Clancy's Rainbow Six (1998), games became more overtly militarized. The solitary hero became a part of the machine. Halo is a kind of bridge between the solitary hero model of earlier first-person shooters and the soldier of later shooters. The Master Chief exists within the military, and to some degree interacts with it, but he's also very much a solitary hero. They're human, he's not, really. As the Halo series continues and its mythology becomes more complex, the Master Chief also becomes more normalized within the human military.
The militarization of the first-person shooter ramped up significantly in the start of the 2000's. In addition to games like Rainbow Six and SOCOM, which used real-world or near-real-world militaries, the real United States Armed Forces started directly creating and releasing video games like America's Army and Full Spectrum Warrior.
This all makes sense, I think, in that widespread internet play made team-based games more appealing. The "deathmatch" of early first-person shooters like Doom, in which every player was against every other player, was replaced by squad-based team games like Team Fortress and especially Counterstrike. As first-person shooters turned into first-and-foremost multiplayer experiences, the setting and storyline had to fit this. Duke Nukem and the Master Chief don't make as much sense if there's 20 of them - but opposing army squads work perfectly. There are also already existing tactics and terms used for such combat in the military, so it's a natural fit.
Nowadays, it seems like every major FPS involves players in some kind of military or paramilitary organization. Gears of War and Halo: ODST do it in the future, while Call of Duty did it in the past and now the present, with Modern Warfare.
Although this makes sense in historical context, it also has the effect of changing the perception of the military and war in video games. The events of Doom and Half-Life are extraordinary, with a lone person taking up a gun and using it to survive. They are the solitary hero because they have to be the solitary hero. In games like Half-Life and Deus Ex, the military forces of the state are the enemy. In more recent games, as members of the military, the player is now a representative of the state. And in order for their premises, settings, and storylines to work, video games have to justify the actions of those militaries. This necessarily means that the violence of the state - war - is now the focus of most first-person shooters, instead of survival. And those wars have to be justified and even glorified for the games to work.
For some people, including myself, and apparently Leigh Alexander, this is discomfiting. It should be.
Addendum: I would be remiss if I didn't mention September 11th, which helped engender a surge of militarism in the United States. I think it was important, and possibly even hastened the process, but I suspect that the move towards squad-based, military-style combat would have happened anyway.