There's absolutely a Renaissance of complicated board games. They rarely rise to the level of Civ for PCs, but can still involve a lot of reading rules / cards. For the die hard fans, they're usually easy to pick up because few games are really 'new'. But for the beginner, telling someone "this is a dice version of Puerto Rico" is useless.
Are there good, easy to learn party games from the past few years? Codenames is a huge hit, and released a Codenames:Pictures followup this year.
Insider is sort of a 20 questions game where one of the guessers knows the buzzword, and must help push the team towards the goal within the time limit without being voted as the insider at the end of the game.
Secret Hitler situates players in 1930's Germany, pitting liberals against fascists in a social climate favoring authoritarian policies.
Sushi Go Party! is a card drafting / set collection game that's fairly easy to explain to novices, and a lot of the appeal is in the variable setup. This version also scales to like 8 or 10 players, if need be.
Captain Sonar is more complicated, but varies with the player's duties (First Mate is considered easiest by my group). It involves two submarine teams hunting one another. The mix of roles i interesting, from easy things like First Mate charging systems, to more challenging roles like Captains navigating the ship without giving away position or Radio Operators tracking the enemy ship and narrowing down their position. Most of the rules are simple, and the rulebook's size is mostly attributable to explaining the more complicated maps. Personally, I like the radio operator, as it's something of a real time Japanese pencil puzzle game.