Yes, past is an adjective following the noun. It's unconventional word order, but this can indeed be done in English.
The inverted word order gives the phrase a grand, majestic feeling. Here, though, the feeling is somewhat ironic, since the point is that Moscow's grand experiments with empire failed. And yes, that really is what the sentence means, although anyone with even a passing acquaintance with Russian history knows it's absurdly false.*
The phrase in times past is actually common enough that everyone has heard it, so placing past after a noun, especially if you're referring to far-off history, doesn't seem like much of a stretch to fluent speakers. This Google search brings up many books that contain the phrase. The OED quotes it as far back as Shakespeare, and the phrase appears to be even older.
* Maybe it just means Putin's attempts to start an empire, or attempts made after the fall of the Soviet Union. But putting past after imperial experiments suggests that one is talking about a long stretch of history, probably centuries, not just the last couple decades.
I see that the article also mentions Putin's "paeans to Muscovy's heroes and greatness past". This is another bit of grandiloquent prose, and clearly suggests a timespan of centuries.