The trade center existed long before 1201 so what exactly changed in 1201? Just church bureaucracy and administration? Or was there a large influx of German settlers that fundamentally changed the layout and economy of the river-port?
The current site of the city of Riga was established as a trading center in the early Middle Ages, but it grew to prominence during the 12th century as German traders began to expand their influence in the Baltic. In an attempt to establish trade routes with the city of Novgorod, Henry of Livonia in his chronicle tells us that by 1158 the Germans had established an outpost there. One of these Germans was Meinhard, a missionary who attempted to convert the local pagan population to Christianity. He settled southeast of Riga at Uxkull, and in 1186 built a stone church there to continue his missionary practice. Eventually, native Lithuanians attacked the church, prompting Meinhard to conscript stonemasons from Gotland to build defenses. Meinhard returned to Germany in that same year to rally support for his mission and was consecrated as the Bishop of Uxkull by the Archbishop of Bremen. By 1193, Pope Celestine III began to take an active interest in the growth of the new bishopric and allowed Meinhard to recruit missionaries and grant indulgences to those who took on this mission. Meinhard had limited early success, but died in 1196.
After Meinhard's death, the bishopric fell to Berthold of Hannover. Berthold attempted to convert by peaceful means, but attacks from the Livonians forced the Christian settlers to flee into their strongholds at Uxkell. This violent action spurred Celestine III and, later, Innocent III to call for action. With their approval, a German fleet was assembled that arrived at Riga in 1198. Berthold sailed up-river to meet the fleet, and was present while the Germans built fortifications for the trading settlement. Berthold attempted to mediate peace between the Germans and the Livonians, but, unable to do so, he sailed down-river back to Uxkell where he was killed in battle by Livonians after a Christian victory.
Berthold, who died in 1198, was quickly replaced by Albert, a canon from Bremen and nephew of the Archbishop there. In 1200 he arrived in Riga with a large fleet. Recognizing that Uxkell was becoming an increasingly difficult position to defend, Albert appealed to have the seat of the bishopric moved to Riga, which was granted in 1201. This act is what "founded" the city of Riga, despite the fact that it had been a trading settlement for some time beforehand. Under Bishop Albert of Riga and the growth of the Livonian Crusade, Riga's population and importance grew. By the time of Albert's death in 1229, Riga became home to a growing number of Christian Liv converts and German traders, a mandated stop along the Baltic trade routes, and the strategic center of military campaigns led by mostly German crusaders, the most prominent of which were the Brothers of the Militia of Christ, known as the Livonian Brothers of the Sword.
Sources:
Christiansen, Eric. The Northern Crusades. 2nd Edition. New York: Penguin Group, 1997
Livonia, Henry of. The Chronicle of Henry of Livonia. Translated by James Arthur Brundage. Madison: University of Wisconsin, 1961.
Smith, Jerry C. and Urban, William L., Translators. The Livonian Rhymed Chronicle. Bloomington: Indiana University, 1977.
Urban, William. The Baltic Crusade. DeKalb: Northern Illinois University Press, 1975.