Apparently, Booth has stolen Mr. Lincoln's hat. Somehow, this has upset the balance of Space and Time and only a pixelated Lincoln can recover all the "pieces" needed to restore that balance.
I'm not exactly sure why the hat holds the key to space/time, or what pieces you are collecting, or why an army of Luchadors is in your way. But, the story of Pixel Lincoln is no more wild than many of the old 2-D sidescrolling action adventure games this deckbuilder takes its thematic inspiration from.
Time to get your beards into gear, friends. This is no laughing matter. The high score itself is at stake.