Take any sort of report like that with a grain of salt. It might just be an artifact due to low amount of Northeast Siberian sample data. Or whatever haplotypes it's attributing to NE Siberians are also present in a portion of Somalians which weren't in whatever sample they used for East African populations and so on (Remember, Africa is the most genetically diverse continent, and so with limited data, you can get all sorts of misattributions because all other populations descendant from African populations and each only shares a portion of the original African diversity.). In a country like Somalia, where you don't have mass movement and urbanization, there's bound to be an abundance of population structure which means representative samples aren't really possible from a few dozen or even hundred people because the population is very, very non-homogenous.

Basically, I'm skeptical. But then again, it could be possible. It doesn't have to be a Yakutsk, but rather someone with partial Northeast Siberian ancestry. There could be a weird route involving the Islamic Turkic khanates in Siberia taking a Yakutsk slave, involvement in the Central Asian Islamic trade system, and then so on until you reach Somalia, which was pretty heavily involved in Arab and Indian trade.

Fascinating question!

I don't know that I can help much, but I may be able to offer a theory — one based on a fragment of my own knowledge. During the 16th and 17th centuries, as Russia expanded into Siberia, it used the yasak system of tribute to collect furs from the Siberian people. Hostages were taken as insurance to the Siberians' good behavior. Many of these hostages were educated in Russian schools or baptized into the Russian church, then returned to their homes. (A similar system was used in the first half-century or so of Russian contact with Alaska.)

The system of yasak was based upon a similar practice used by the Golden Horde of the Mongol Empire. Now, I'm not familiar with yasak as practiced by the Mongols, but if it was not too dissimilar from the Russian practice, it is possible that a Sakha person could have been taken as hostage by the Mongols and traveled south and west.

It's also possible that simple trade routes and traveling traders could be to blame, but I don't know enough about that to comment intelligently.

You're asking about genes, not culture. There's no need for a direct cultural interaction to happen. A Mongol could've married a Yakut, his descendants could've travelled in the Genghis Khan's army further west, like /u/The_Alaskan suggested, his descendants could've intermarried with local Persians or Arabs, and finally their descendant, culturally and visually Arab, could've interacted with Somalians and spread his partially Yakut genome.

I think the other theories are more valid than this one, but I just thought it would be interesting to share it with you.

Russia took part in the Scramble for Africa at the end of the 19th century and colonised Djibouti for a very short period of time (1889). It was called Russian Somali. Although the mission failed badly and it didn't cause a lot of change in that area, it could be an explanation.