I haven't looked closely at the study, but I did study Y-Chromosome patterns a while back (at least at a wikipedia-level of depth... I'm not a geneticist either). Once you start looking into the details, it quickly becomes apparent just how much moving around and intermixing people did in the past, to the point that its really rather quite amazing that there's still any such thing as distinct races today. From what I see, a large number of Romani belong to
haplogroup H, which is also present in certain parts of south India, and very rare outside of these groups.
Meanwhile, it is
haplogroup J that contains many of the
Jewish people, including many Ashkenazi and Sephardic, as well as the supposed "Cohen gene" and the handful of
Samaritans that still live in Israel (
I didn't even realize there were still Samaritans). However, J is bigger than just Jewish people. It really encompasses many of the peoples living in the Middle East, including high percentages of Arabs, Iranians, Kurds, Syrians, Palestinians, Yemenese, etc... From a Genesis perspective, I'd say this haplogroup correlates with someone between Shem and Abraham. Thus I would expect any lost tribes of Israel -- if they truly have patrilineal descent -- to have a high incidence of haplogroup J in their population. That said, many of these groups also contain a high proportion of haplogroup E -- especially E1b1b1. Since this group is also found throughout north and east Africa, I can only conjecture that this may represent either the mixed multitude that accompanied Israel out of Egypt, or the mixture of Hamitic Canaanites peoples. Ashkanazi's also contain some amount of G (found in Georgia and Caucasas), R1 (generally IndoEuropean), and oddly Q (Siberian and Native American), all of which I imagine would probably indicate mixture with host populations throughout the diaspora.
As an example of the kind of mixture I'm talking about, native Indian populations contain significant percentages of haplogroups C (seemingly migrated from Africa or Arabia), H (focused in the south), L (focused along the Pakistani border), T (in the East), and R (Indo-European, and seemingly originating from SE Asia). And I'm probably missing some.
Another example: There's a haplogroup I, which is a sister-group to J, which might make you think that it's also Middle Eastern, except it's not -- it's concentrated in South Eastern Europe (Bosnia, Croatia, Serbia, etc...) and Scandinavia, and spread to a lesser degree throughout the rest of Europe. This might make you think this group was Slavs or Vikings or even Germanics or Celts or something, except those were all Indo-European groups (mostly R1). Presumably, hg I would have been whatever indigenous people were in the area
before the Indo-Europeans arrived. Add to that the arrival of North-Asian Uralic/Finnic people that had mostly N haplogroup, Jewish and Arab immigrants (mostly J and E), other peoples from the Caucasus (F, G, K), the Roma immigrants from India (H), and the inexplicably-ubiquitous low-levels of T, and Europe is all over the place.
(BTW Addleman, the creator of the 1st DNA computer is Jewish 
