Why didn't trench warfare produce a similar stalemate on the eastern front in World War I?

To frame what the OP is asking the question is "Why didn't the Eastern Front devolve into an attritional conflict like the Western Front?" we need to examine what were the tactical and operational reasons for the devolution of warfare into stalemate.

The two obvious and interrelated causes are: 1. Space and 2. Command and Control.

Space: By the beginning of 1915 warfare on the Western Front had devolved into a stalemate as a result of the Race to the Sea which meant there was no potential for maneuver to achieve the upper hand. However this was not unique to France, and we can see the same result for example in the Dardanelles Campaign. The terrain did not permit manuever so the conflict become a war of attrition. Another poster also mentioned the Italian campaign.

Command and Control:

It seems to surprise some but the ability to control large armies (one hundred thousand plus) simply didn't exist before the end of the First World War. Even with the space to maneuver, the Americans found in the Civil War that it was not easy to achieve a breakthrough when faced with significant defenses (see the Seven Days Battles).

In fact the Americans never really were able to develop sufficient ability to command large bodies of troops nor manage their logistics during that conflict, rather it being won through the far superior industrial capacity of the North rather than the evolution of the operational art. We see similar results in the excessive casualties suffered by both sides.

Another example of command and control hindering the offensive movement of an army occurred at the First Battle of Gaza. The Australian Light Horse were able to enter the city at the end of the day, but were withdrawn due to concerns regarding Turkish reinforcements and poor communications. In fact communications played a very large role in poor C&C in WW1.

the Russians slower to adopt trench warfare tactics than the Germans, British, or French?

It was less necessary. After all, what pressing reason would the Russians have for adopting trench warfare? They remained on the offensive, strategically speaking, for the duration of their involvement in the war. Simply remaining on the defensive in the East would've suited the Central Powers war aims perfectly - that is to say the Germans were seeking a decision in the West before turning to the East to fight the Russians.

The Russians had a strategic imperative to attack in the East in order to prosecute a two-front war (which is ultimately what cost the Central Powers the war). Not attacking would've played into their hands. Their alliance with the French also obligated them to take the offensive. It's also important to note that in the Galician Campaign, the number of trains that were able to available to the Russian to transport materiel to the theatre

The Russians could bring 260 trains a day to their front, compared to the Austro-Hungarian's 152.1

Another interesting point is that there were significant forces crammed into Galicia, despite the front being only 260km long, the Russians were able to achieve a decisive victory in a matter of months.

The East Prussian campaign also offers another insight into how strategic imperatives influenced the prosecution of the campaign. Due to the unique shape of East Prussia being connected to the rest of the German state by the Danzig corridor, the Germans were simply unable to conduct a passive defence and used their rail networks and superior command control to execute a devastating counter offensive that utterly annihilated Samsonov's 2nd Army.

Both the ability (or lack thereof) to control large armies and a lack of "strategic" space is what often caused a devolution to trench warfare. However, these factors alone did not drive a devolution into attritional warfare. We also know that the industrialization of warfare and Europe also presented difficult tactical and operational challenges that took officers on both sides some time to learn how to over come. The vast resources available to both the Allies and the Central Powers also ensured that the war was never going to be settled with short battles of maneuver.

A young Charles de Gaulle, already wounded twice, grimly observed in December 1914: “What is this conflict but a war of extermination? A struggle of this kind, which in its range, significance and fury goes beyond anything that Europe has ever known, cannot be waged without enormous sacrifices. It has to be won. The winner will be the side that desires it most ardently.”

Technology also played a part. Warplanners on both sides made faulty assumptions that led to miscalculation when the war started. For example:

Alfred von Schlieffen’s vision of a grand envelopment was impossible because the technologies of mobility and communication lagged far behind the destructive power of 20th-century weapons. “In the pre-motorised age, defenders proved able to redeploy and reinforce more swiftly than attackers advanced, by the exploitation of rail links. It was a disastrous collective delusion, to suppose that a formula could be identified for achieving quick victory over three of the greatest powers in Europe…Rather than a strategist of genius, Schlieffen proved to be a fantasist who brought doom upon his foolish disciples.”

This article from The Economist lays out some great texts that cover a lot of aspects of the war, and is worth perusing if you are looking for further read on the topic. 2

This article also outlines how many battles on the Eastern Front were battles of maneuver rather than attrition. Simply put, the Eastern front allowed opportunities for maneuver that the West did not. http://warontherocks.com/2016/07/slaughter-on-the-somme-the-limits-of-foresight-on-the-road-to-the-great-war/

[please not this answer is only a first draft, and it is 3am here, and I'm having a glass of wine, typing on a keyboard without a space bar - I do apolgise for what is in my mind a rather terribly written post - expect it to be revisited over the next 24 hours.]