It's a great piece of writing, but most people miss a big part of the speech: a lot of the speech is a defense of the idea that you can have a country that isn't a monarchy. At the time the political elite in most of the world (aka: Europe, nobody white/important cared about silly little non-white countries in incredibly racist 1863) was strongly convinced that if you didn't have a person with a hereditary claim to the top job in the land that person wouldn't be respected, which would mean that the inevitable factions that arise in any country would split it apart.
Their evidence was (at the time) pretty good. No European Republic save the Swiss and Dutch had managed to thrive on a long-term basis since the Middle Ages. The Dutch had gone over to a monarchy, and the Swiss were a) tiny, and b) had just experienced their own Civil War in 1847.
In terms of Non-European white countries, most of the Americas were Republics. But even here Republicanism was losing ground. The Brazilians were an Empire dominated by the Braganza dynasty. The Dominican Republic granted itself back to the Spanish Crown in March of 1861. The Mexicans had invited a Habsburg Archduke to become their Emperor in 1864. The new colony of Santo Domingo was gone by the time Lincoln the confederacy fell, but the Restoration War started in August of 1863; the Mexicans didn't shoot their Emperor until '67 and the Brazilians were a monarchy until Pedro II freed the slaves in 1888.
What seemed to be going on was that conservatives didn't trust a President to protect them from radical reformers, and mid-19th century radicals could be really crazy, until the US managed to hold itself together for a few decades. Once those famous four-score and seven years resulted in the country splitting many decided they needed a monarch. When Lincoln won they changed their minds.
Below the fold is the text of the address, with the pro-Republican points bolded and explained a bit.
Four score and seven years ago our fathers brought forth on this continent, a new nation, conceived in Liberty, and dedicated to the proposition that all men are created equal.
The last sentence in this paragraph is probably one of the earliest quotes from an American statesman, in a one of the documents every American feels guilty for not knowing by heart, that implies that slavery was un-American.
But it's also a denunciation of monarchies where only a tiny minority has any shot at the top job. He's implicitly claiming that countries like the UK, and modern Canada (which was not independent until 1867, another knock-on-effect of the Civil War) are inherently less free then America because we're a Republic and anyone can become head of state even if his father was a total loser. Obama actually wrote a book about how his mom was too good for that deadbeat, lying, Kenyan, Alcoholic she married when she was a teenager.
Now we are engaged in a great civil war, testing whether that nation, or any nation so conceived and so dedicated, can long endure. We are met on a great battle-field of that war. We have come to dedicate a portion of that field, as a final resting place for those who here gave their lives that that nation might live. It is altogether fitting and proper that we should do this.
This is a clearer reference to the controversy.
The whole point the monarchists were making was that a nation with no dynasty to unite it couldn't survive.
But, in a larger sense, we can not dedicate -- we can not consecrate -- we can not hallow -- this ground. The brave men, living and dead, who struggled here, have consecrated it, far above our poor power to add or detract. The world will little note, nor long remember what we say here, but it can never forget what they did here. It is for us the living, rather, to be dedicated here to the unfinished work which they who fought here have thus far so nobly advanced. It is rather for us to be here dedicated to the great task remaining before us -- that from these honored dead we take increased devotion to that cause for which they gave the last full measure of devotion -- that we here highly resolve that these dead shall not have died in vain -- that this nation, under God, shall have a new birth of freedom -- and that government of the people, by the people, for the people, shall not perish from the earth!
The clearest reference of them all.
A Southern victory wouldn't have forced the North to actually change anything about how Ohio was governed. But it would have made the principle of government by the people (ie: having a President elected from the people) look really bad.