I don't think anyone is complaining about the shooting in of itself, the issues are the conflict with the characters and story. In COD, you're a soldier so it's expected that you can kill people with little effect. The characters themselves are relatively blank anyway. Also the narratives in COD aren't exactly held in the highest regards and in general, really aren't intended to be taken very seriously. The issue with TR is the focus on the narrative and characters. The violence seemingly isn't done in some sort of insightful manner or parody and thus any sort of strong contrast or conflict is highlighted.
You're splitting hairs. The cognitive dissonance that exists in videogames where we have "likeable" protagonists maiming a micronation worth of people in order to progress through a story has always been absurd. The difference now is that Lara Croft is presented, initially, as a fragile young woman down on her luck. But almost all the reviews so far show that, at some point in the narrative, Lara emerges as the heroine and the game becomes revenge porn. In that way, the violence is meant to thrill the viewer, the same "fuck yeah" mentality that has driven Quentin Tarantino's career for decades.
There a few reasons I think Tomb Raider in particular is getting attention.
a. It's a shift in tone for the series. The violence has always been overplayed, but so too has the cheese and the mythical elements. Campiness allows the consumer to forgive a lot of violence it might not otherwise.
b. Lara is a woman. I'm not saying this is the main reason or anything. But seeing her character preform death defying stunts regularly and kill without remorse is jarring compared to the archetype we are used to. When it's a man with beefy arms, we know he is "programmed" for violence and his physicality is obvious so we can expect the ridiculous stunts.
c. Crystal Dynamic's PR team suggested that this game would both be empowering to women and that the "player would want to protect Lara." These are contraries. A male empowerment fantasy includes "save the damsel." Still, I think this is more an imagined error, and it's mostly the fault of assumption on gamers part, and Crystal Dynamic's perhaps saying too much instead of letting the game speak for itself.