Because nationalist Russian historians liked to claim that it was the end of the Tartar Yoke, even though it was not exactly the end of the Tartar Yoke
It is possible that the Tatar Yoke did not finally end for two centuries after the standoff on the Ungra River, gradually becoming weaker and weaker. And one could claim metaphorically that the Tartar Yoke continued until the February 1917 revolution, now being enforced by Russian rulers to benefit themselves.
The reasons given by Semaphore and T.E.D. for considering the standoff on the Ungra River the end of the Tartar Yoke are strong.
Another reason for claiming that is Russian nationalistic pride. Proud Russians would like to claim that that Tartar Yoke was lifted as soon as possible, regardless of historical accuracy. Thus one may wonder whether the standoff on the Ungra River really was the end of the Tartar Yoke or if Russian historians jump the gun claiming that it was.
I note that Alatoo's deleted answer says: the Tatars ran away and Russians just left after the Tatar threat was gone.
On October 28, Ivan gradually started to pull his armies back to Kremenets for winter quarters. Akhmat waited for reinforcements until November 11 and then turned south.1
Thus it seems that Ivan had to retreat from the oncoming winter weather 14 days before Akhamt retreated to his homeland. Thus Alatoo seems to have have reversed the order of retreat, perhaps out of Russian nationalism.
In nationalist history, the Ugra Standoff is taken as the end of the so-called "Tatar Yoke". Modern writers are more skeptical and see it as an important landmark in the gradual expansion of Russia and the gradual decline of the Mongol empire.
Thus the Tatar control of Russia may have become slighter and slighter, weaker and weaker, over several centuries before and after the Stadoff and the Ugra River.
I believe that the Tatars sometimes demanded tribute and other facets of over lordship from the Russians after the Standoff on the Ungra, and that they sometimes succeeded in their demands. In 1571 the crimean Tartars burned Moscow except from the Kremlin, and it was said that only 30,000 survived out of a population of 200,000, and made and unsuccessful attack in 1591.
Since the Russians didn't always have the military advantage, they may have sometimes agreed to pay tribute to Crimea.
The treaty of Constantinople in 1700 ending the Russian-Turkish War of 1686-1700 included a clause abolishing the annual tribe from Russia to the Crimean Khanate.
The Treaty of Constantinople (1700)brought a formal end to the annual tribute delivered to the Khan, rather grudgingly, by the tsars, and in 1768 Crimean horsemen conducted their last slave raid into Russian territory.
1700 Peace of Constantinople. Russia retains Azov and Taganrog. The Russian Tribute to the Crimean Khanate is abolished.
In addition, the Turks repudiated the Crimean khan's claim to an annual tribute, so much resented by the tsars: it had not been paid since 1683 and by 1700 the arrears amounted to perhaps a twelfth of Peters revenue in that year.
So the New Cambridge Modern History Volume 6, page 627, claims that a tribute to the Tatars was last paid in 1683, 203 years after the standoff on the Ungra River. The source is given as Sumner, page 77n.
Thus I suspect that Muslim or Turkish historians may often claim that Russia was legally a tributary of the Crimean Khanate - which was a vassal of the Ottoman Empire - on and off until 1700, 220 years after the standoff on the Ungra River.
I guess that some historians could claim metaphorically that the Tartar Yoke was not lifted until the February Revolution in 1917, soon to be replaced by the Communist Yoke in the October Revolution.
The Princes of Moscow became the Grand Princes and Tax collectors for the Golden Horde. And they used that position to tyrannically usurp more and more power from the other princes of Russia. Thus they may have dragged their feet in revolting against the Mongols and used the Mongol threat to justify collecting taxes (to keep the Mongols from devastating Russia) until their control of Russia was strong enough that they could keep on collecting taxes and oppressing Russians without Mongol backup support. Thus after revolting from the Tartars the Russian grand princes and Tsars continued the Tartar yoke and oppression even after gaining independence from the Tartars. Thus one could say the Tarter Yoke continued, now being imposed by Russian rulers.