It's not often that words fail me, but in this case I think they might. There's just no way to fully describe the variety of reactions that I get when playing this game. I can describe SOME of it - enjoyment, amusement, mild frustration, more amusement - but more than anything this is something I simply did not expect in a Serious Sam title.
Briefly, the game plays a bit like a classic turn-based RPG, with you selecting actions (primarily attacking) while facing off against enemies. What makes this a Serious Sam game is that it's initally just Sam against 20+ enemies per encounter, and you're running backwards as they're running towards you. The format is also a bit different in that you can move Sam around as wave after wave of enemy heads towards you, allowing you to dodge attacks, or try at any rate. As you progress through the game you gain two other allies who you can control during fights. This improves your damage output but makes dodging much harder, as all three move as one unit. In between fights you move around on an overhead view map, encountering enemies randomly as you move; thus, the name.
Of course, what also makes this a proper Serious Sam game is the weapons you are given. Initially limited to a Revolver and Minigun, you eventually pick up nearly the full compliment of Serious Sam weapons: shotgun, rocket launcher, laser rifle, sniper rifle, grenade launcher, and even the Cannon. Each has been balanced fairly well for the way the game plays, with differing strengths and weaknesses. Last but not least, the game has no shortage of humor, perfectly on tone for Sam and his usual shenanigans. Many of the jokes are aimed at the game's new format, with Sam complaining about "puzzles" (read: having to pick up a key) for example.
In the end, Serious Sam: The Random Encounter is an amusing and enjoyable spinoff of the Serious Sam brand, though admittedly a very short one. On my first attempt it took me about an hour to get through the entirety of the game to the final boss. I won't say that's a dealbreaker, especially since the game has a reasonable replay value, but it's worth knowing when you're deciding how much you're willing to pay for a copy. If you need something to kill an hour or two, you could do far worse.