Yes, Stalin killed people of all backgrounds. But so-called reactionary nationalities were specifically targeted for NKVD operations. For example, the NKVD would round up people with Polish-sounding names from telephone books during the Great Purge. Entire peoples were deported to Central Asia—you can't deny an ethnic dimension to his Terror.

Whatever Stalin's initial intentions were for the Doctors' Plot case, it ended up taking on a clearly antisemitic character, with the media hyping up the threat of Zionism. We may note that while Khrushchev denounced the Doctors' Plot as having been fabricated by Stalin, he didn't denounce the antisemitic rhetoric.