According to Rashi - and confirmed by the Maharsha (as pointed out by samsam) - it's a collection of Oral Law passed down over the generations to explain דברי הימים - Chronicles. It was not a book detailing [then] current Yichus.
Most of Chronicles consists of lists; these lists need explanation.
אָדָם שֵׁת, אֱנוֹשׁ
This Pasuk (Chronicles I 1:1) is a father-son list:אָדָם the father of שֵׁת the father of אֱנוֹשׁ.
Now look at Pasuk 1:4
נֹחַ שֵׁם, חָם וָיָפֶת
This Pasuk lists Noach and his 3 sons. So the Book of Genealogies would enable one to create a Family Tree from the lists of Pesukim.
As the Gemara itself says that between Ezel and Ezel they learn wagon fulls of Halachot. If you look up the verses in question they are very similar:
the first Pasuk is from Chronicles I 8:38
וּלְאָצֵל, שִׁשָּׁה בָנִים וְאֵלֶּה שְׁמוֹתָם עַזְרִיקָם בֹּכְרוּ וְיִשְׁמָעֵאל וּשְׁעַרְיָה, וְעֹבַדְיָה וְחָנָן; כָּל-אֵלֶּה, בְּנֵי אָצַל
The second Pasuk is from Chronicles I 9:44
וּלְאָצֵל, שִׁשָּׁה בָנִים, וְאֵלֶּה שְׁמוֹתָם עַזְרִיקָם בֹּכְרוּ וְיִשְׁמָעֵאל וּשְׁעַרְיָה, וְעֹבַדְיָה וְחָנָן; אֵלֶּה, בְּנֵי אָצַל
So they had wagon fulls of explanations for the 40 verses between these 2, and/or for the reason for the repetition and slight change between the 2 verses.