I first got interested in this period via the Russo-Turkish War of 1877-1878, which I discovered as a teenager and loved for its exotic obscurity as much as anything. From that, I then got into all the other 'hyphenated wars' of the later nineteenth century, including FPW.
As for why I am still interested and what makes it great for gaming, I can do no better than to quote the introduction to the 'Bloody Big BATTLES!' ruleset that was first created expressly to enable recreating the major FPW battles easily and in their entirety:
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Why is this period so interesting? To answer that, consider the Napoleonic era which precedes it. By 1815, after 25 years of continuous continental warfare, broadly the same weapons and tactics are common to all European armies (albeit some are better at using them than others). The ‘holy trinity' of protection, mobility, and firepower, as embodied by the three arms of infantry, cavalry, and artillery, is in perfect balance, making battle a kind of complex exercise of rock-scissors-paper between very similar forces.
But as the century wears on, disruptive technologies appear: breech-loading rifles in the 1840s, breech-loading rifled artillery in the 1850s, machine-guns and repeating rifles in the 1860s. And not only weaponry, but also railroads, steamships, ironclads, the telegraph, observation balloons …
And while technology develops apace, most nations spend most of the time at peace. Consequently, each time a war breaks out, the protection-mobility-firepower equation has been modified, and each time, the armies engaged have to learn new lessons the hard way – in some cases, the wrong lessons, which then cost them dearly in their next conflict.
The bad news for the troops is that constant improvements in weaponry mean that maneuver under fire becomes more and more difficult, and battle gradually reduces to a contest between firepower and protection. This eventually reaches its apex in the static trench warfare of the First World War, with mobility squeezed out almost entirely.
But the good news for wargamers is that, for the few decades we are interested in, tactical maneuver persists. War continues to be decided not by long weeks or months of attrition across hundreds of miles, but by decisive clashes between whole armies lasting usually no more than a day or two. These are fought on battlefields just a few miles across, making it possible to capture an entire battle in one tabletop miniatures game.
Furthermore, the evolution of weapons and tactics means that many of these conflicts pit opponents of very different character against each other, making for some fascinating interactions at the tactical level.
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In short: big, decisive battles, between asymmetric opponents, which means lots of variety and lots of interesting tactical challenges.
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