We're not arguing if the act of playing a game could make you misogynistic.
I misinterpreted that a bit, clarified below:
I fail to see the connection between the first and last part, but I'd be interested in hearing more about your reasons for believing that. Could you perhaps elaborate?

(My own opinion is that I'm totally unsure on what to think of Love Plus
in the context of this question, so I really would like to hear your opinion on this!)
Wiki:
Misogyny is manifested in many different ways, from jokes to pornography to violence to the self-contempt women may be taught to feel toward their own bodies.I actually only used the last part to define misogyny, (wo)men view themselves negatively. So I guess Love Plus does not fit in all areas of the Misogyny spectre. Nor does Love Plus directly teaches or imply males to feel negative about their body (in misandry), but I think it there is a correlation between the stereotypical Love Plus player and his (non-existing) self-confidence due to negative view of the self.
RE: Tomb Raider
I see that point. And I understand, to a degree, that she is portrayed as a strong female lead. But what, if any, of her "female qualities", if you will, are portrayed? It's not "none" (which would be okay, I guess - more like Mass Effect's (female) Shepard, perhaps?) - is it "appearance" (which could be argued means objectifying)?
Do women have other qualities then? :-D *hides cowardly*
As an addendum, it is worth nothing how extremely different the google-results are:
Earhart,
Croft,
d'Arc. Yes, the context and audience of their stories are very different, but you cannot deny that there is a difference here. What meaning lies in the essence of this difference?
"context and audience of their stories are very different", did you mean similar? Otherwise I might be misunderstanding you.
"What meaning lies in the essence of this difference?".
Jeanne 'd Arc and Amelia Earhart became an icon by showing a strong female will, motivation or drive to reach a goal in an "unfriendly" environment (male based (science/war) world) as a war'lord' and pioneer in aviation. So in general, a woman's mental strength. (I guess)
The main difference between Lara Croft and the above heroines is her attitude. Her famous fierce pose (hip a bit to the side, guns in hands) is mainly what made Lara Croft an icon in women heroine history. It's equal to Tanya from Red Alert (throw up both guns in the air and scream fiercely when shooting). These heroines are about visual aesthetics, how to make a fierce visual impression. I feel I say fierce too much. I am also sure their artists put a lot of thought in the way they pose. This became more important the last twenty years in our society, so the focus is now there. Doesn't necessarily make it sexism or misogynous at all. Although it is an ideology, it's not a negative one (which I feel sexism and misogyny are).
So I guess you are not that far off in saying Lara Croft's main female quality is "appearance". And that is perhaps objectifying, but that does not make it sexism or misogyny either. Being an icon is being objectified. You become part of an ideology, but that could also be a positive one. You don't need a sexy pose to be an icon, wearing a fancy sci-fi suit will do too. Commander Sheppard is perhaps a new icon in female ideology: the power of being modest (she's not that sexy dressed, but still a favourite among gamers due to her 'efficient' way of handling things... hence becoming a Spectre).
Granted, Natasha and Tanya in Red Alert 3 makes quite a lot more sexism.