Okay, here's what I've tried so far. Seems to work, but I'm worried about how long it will take for 10000 titles. So, you may need to figure out how to improve performance.

Assuming you have saved your word doc in rtf format, start by importing it into Mathematica:

rtfNotebook = Import[pathToFile]

This will give you a notebook expression, which is interesting. You could open it as a notebook and start working with it as if it were just another Mathematica notebook. But you can also just manipulate the notebook expression directly (which is what I'm going to do below).

Inspecting this notebook, it does look like anything that was italicized in the original is now represented as a StyleBox with the option FileSlant->"Italic". We can extract all of these with Cases:

Cases[rtfNotebook, StyleBox[___, FontSlant -> "Italic", ___], Infinity]

Here's one example of what you'll see in the result:

StyleBox["Thermus thermophilus", FontFamily -> "TimesNewRomanPS-ItalicMT", FontSize -> 18, FontSlant -> "Italic"]

All we care about is the string content part of the StyleBox, which should always be the first element. We can get Cases to extract that for us as well. While we're at it, let's save the result in a variable:

italicizedPhrases = Cases[rtfNotebook, StyleBox[content_, ___, FontSlant -> "Italic", ___] -> content, Infinity]
(* {"Thermus thermophilus", "What is life", <<7>>, "Thioreductor micantisoli"} *)

You want two word phrases, so let's use Select to find those:

candidateBinomials = Select[italicizedPhrases, (2 == WordCount[#]) &]

I don't know if further processing will be necessary, but I was curious about whether Mathematica recognized these as species:

species = SemanticInterpretation /@ candidateBinomials

It did indeed! Here's an example of one of the entities it returned:

Entity["Species", "Species:ThermusThermophilus"]

I wondered what Mathematica might know about species:

EntityProperties["Species"]

Looks like it might know the taxonomic sequence, so I tried that:

EntityValue[species, EntityProperty["Species", "TaxonomicSequence"], "EntityAssociation"]

From this I learned that Thermus thermophilus is a bacteria with this taxonomic sequence: bacteria -> hadobacteria -> Deinococci -> Thermales -> Thermaceae -> Thurmus -> Thermus thermophilus

Here's what I would try, but without specific data to test with, I can't be sure how successful this will be.

Save the doc as rich text (.rtf). From Mathematica, use the Import function to import the rich text doc. I think that what you'll end up with will be an expression that has the formatting stuff represented as StyleBox expressions. From that point, it's a matter of writing a function that will recognize those StyleBox expressions that are used for the species binomial. With that function, you would then search (with Cases maybe) the whole imported expression for the matching StyleBox expressions.

Alternatively, Mathematica has SemanticImport and SemanticInterpretation and other related functions. This feels like a stretch, but maybe there is some way to use those that just automatically picks out species binomials from a given text.

Maybe if you provided a snippet of the document we could test these ideas.