While their rulership was miserable, to put it mildly, I think the appeal is that that is when Russia was expansionist. They were conquering Irkutsk and Siberia.
Think of the American drive westward in the era of Manifest Destiny. We Americans will pat ourselves on the back and tell ourselves just-so stories. The Russians have that mythos in their own history too, to an extent. Their eastward expansion into Siberia is a story that hasn't really been told here in the West, but it captures much of the same vibe.
Russia was actually industrializing at a good clip in the late-19th/early-20th century, too, according to Paul Kennedy in
Rise and Fall of the Great Powers. Remember, that although their track-mileage and steel output was far behind America or the UK, they could still build battleships, and indeed
built the first heavy bomber in the world.
Imperial Russia was a time when Russia had stature in world affairs, and swung some weight even after their defeat in 1905. Putin is, I think, trying to redress their significant loss of gravitas over the last thirty years, while trying to avoid the potential allusions to the dissolution of the USSR. In other words, he's going far back enough that arguing the facts will be hard, and so instead he gets to promulgate the myth unfettered.
That's my take on it.