The Marx & Engels Internet Archive for the year 1869 indeed has correspondence between the two innovators of scientific socialism dated 17 December of that year, but it concerns Irish trade unions-- i.e. a totally different topic. [1] I'm not trying to call into question your source's validity here, but I'd love to see some more of that letter to get a better understanding of the context of what Marx is talking about specifically.

Barring that for the time being though-- it's important to point out, Marx's general opinion wasn't so much anti-Russian as anti-Romanov and anti-Tsarist. He viewed the Russian autocrats extremely negatively, but had enormous sympathy for the actual oppressed masses of Russian peasants and proletariat.

Engels noted in a letter to the famous Russian singer Madame Evgenia Paptriz:

We both, Marx and myself, cannot complain about your countrymen. If in some groups there was more revolutionary muddle than scientific research, there was also, on the other hand, critical thought and disinterested investigation in the field of pure theory, worthy of the nation of Dobrolyubov and Chernyshevsky. [2]

Issac Deutscher, a celebrated Marxist intellectual from Poland, likewise noted in a 1948 essay entitled Marx and Russia:

Broadly speaking, [...] Russia was to Marx still identical with Tsardom, and Tsardom was the hated 'gendarme of European reaction.' His and Engels' main preoccupation was to arouse Europe against that gendarme, for they believed that a European war against Russia would hasten the progress of the West towards socialism. [3]

Deutscher is basing that claim on correspondence between Marx and Engels that had become available the year before he wrote the aforementioned essay spanning 1846 to 1883, so the period your source is from as well. As such, I don't think it's unreasonable to suggest that in this specific case, Marx is likely trying to say a resurgent Romanov dynasty would catalyze increased autocratic oppression upon the masses and signify a tangible step in the opposite direction of the socialism for which he advocated-- the devil to to pay, in this case. Remember Marx died in 1883-- nearly four decades before the Bolshevik Revolution of 1917.

Also important to note, the organization which released the correspondance Deutscher referenced (and likely the publisher of the letter you're referring to as well) was the Marx-Engels-Lenin Institute, about as close to the official archival and doctrinal mouthpiece of the Communist Party that you're going find. Suffice to say, the Bolsheviks were totally onboard with what Marx was saying about Russia in the 1800s.

One additional viewpoint Marx held which could be construed as broadly anti-Russian was his strong sentiment against pan-Slavic and specifically Russian nationalism which was present among some of the thinkers with whom Marx interacted. I don't think it's fair to equate that to Russians in general though, as Russian chauvanism and a desire to expand and incorporate other Slavic peoples and territory was an explicit feature of parts of the emigre community. Many of these people (which included Bakunin and his supporters) were involved in organized resistance to Marx's own work. [4]

As such, the answer to your question is rather anticlimactic, Marx wasnt't especially anti-Russian, but any sentiment he maintained against the state of Russia vis-a-vis its autocratic ruling class was completely supported by the Bolsheviks-- including figures like Vladimir Lenin and his ilk.