The trick to the Sticks-style improv games is giving the cards in the card stacks enough mechanics to make the game playable, introduce one or two new pieces of gaming technology and give them works that spark ideas to hang idea hooks off of. This is easier than it sounds.
First off, by sticking to clearly defined genres (such as d20 Fantasy) no one has to explain much - we all know what elves and dwarves are and there's no having to explain what an Ahoggya is or how the religious chaste system operates.
Second, a decade+ of d20 D&D did a really good job of boiling D&D down to its bare essentials (Six stats, which gives bonuses to rolls; Skills or Proficiencies gives bonuses to rolls; success and failure are d20 + bonuses against target number; sometimes degree of success has a separate die roll; high is always good). Adding new pieces of game tech onto that, such as changes to the magic system, or mook rules, or fan mail, are really simple given how simple and robust that base is.
Third, it takes remarkably little to get people to build off of when designing their characters. There are always 3 types of each class card (so 3 fighters, 3 clerics, 3 rogues and 3 wizards) and what I ope to call those makes a huge difference - the first time we played I called the Clerics Exorcists, Crusaders and Thaumaturges and huge amounts of the session were driven by how the players of cleric PCs took them and spun off the evocative terms. In the second game I had the Clerics decide how much affinity they had with Odin, Thor, Loki, Freya and Baldur - the game didn't become Norse, but the connotations around those gods immediately changed how the politics played out.
Inevitably the players come up with character ideas that I would never have considered when pre-generating characters, and likely that the players wouldn't have come up with if I'd given them a detailed world history. In many cases restrictions breed creativity, but so far with this the open endedness of these one shots, the players ability to draw parts of the map of the world, define how they know one another however they want, and merge together the general concepts of the combined cards make the whole thing so exciting to me as a GM. I literally have no idea what they're going to come up with for the day, and neither do they.
I think this time I'm going to focus on evocative class titles (tomb raider, cartographer, foreign legionnaire and missionary will show up at the very least). Then the concept of effect rolls being more than damage - you still roll a d20+ bonuses to see if you succeed in, say, climbing, but the quality of your tools determines whether you're rolling a d4, d6 or higher for how well you did. This takes an existing, well understood mechanic and apply it to other things (you need 12 points of effect to climb this wall), which as I think of it might let you combine things, so morale attacks would directly reduce opponent's effective Hit Points the same way damage does to see if they stop being a threat. That has legs as a mechanic, but it's rooted in the d20 idiom so there's little new to learn.
There will also be some of the ideas I've been working out for what magic should be used for in a dungeon crawl game (low level magic lets you overcome lack of preparedness or loss of gear - Light spell lets you survive without torches, while Mount lets you recover from your horses being eaten) added to higher level magic being more like versatile powers (you have flame magic - what can it do?) This sort of magic is critical as the characters get more powerful as no one has time to absorb and memorize the spell lists in our 5 hour game slot.
I have about 6 weeks to work out the specifics, but i like where this is going.