Like most Knizia designs, Tutankhamun is driven by conflict between players as they attempt to satisfy their desires. You each start the game with a clean slate and no attachments, but as the game progresses, you acquire artifacts to offer to the recently deceased Tutankhamun and you want your offerings to be better than those of others so that you can "cleanse your spirit" — that is, reduce your score to zero — first.
To set up the game, lay out the eighty tiles in a path that represents the Nile, with the players' ships at the head of this path. Each player starts with 18-30 spirit points based on the player count.
On a turn, move your ship any number of spaces down the path or backwards to the tile immediately behind your ship. If this tile is an artifact, collect it; if it's a god tile, use the god's power. If all artifacts of the type you just collected have been claimed by players or removed from play, score that artifact, with the majority holder collecting as many points as the number of tiles of that type in the game. Whoever has the secondmost tiles of this type scores half this amount. If players are tied, whoever is farthest back on the path — that is, closest to the starting position — wins the tie.
If all players have passed one or more tiles, then tiles are removed from the path one by one and placed in the Underworld, triggering if the last tile of a particular type is removed from play.
When a player reduces their score to zero, at the end of the turn they win the game. If multiple players go to zero on the same turn — which has happened once in the seven games I've played on a review copy from 25th Century Games — then whoever is farther back on the path wins.
In a two-player game like the one above, removed tiles in the Underworld serve as a "third player" of sorts when determining who has the most tiles of a type. Sometimes you can move past the right tiles, dumping them in the Underworld and consigning your opponent to second place in a type that they spent time collecting. My gut feeling tells me you want at least 2 points per tile that you collect, so if you can force someone to score less than that (while you're hitting that target), then you'll come out ahead in the end...maybe.
That qualifying "maybe" is in place because Tutankhamun gives you the freedom to move anywhere on the path. Have seven of eight tiles been claimed or removed with the final tile located three-quarters of the way down the path? You can take a huge leap onto that space to claim the final tile, which then triggers a scoring. One of the god powers allows you to move your ship to the back of the path, so a move like that is possible — even desirable since it catches other players off guard, akin to a football quarterback who normally dumps screen passes suddenly launching a bomb halfway down field.
The beauty of this game is that openness that allows you to do whatever seems right at the time. The move might turn out to be a disaster, of course, depending on what everyone else does, but like many Knizia designs, this one allows you to make unpredictable moves that tilt the playing field and force everyone else to respond to what you're doing. For good or bad, Knizia designs give players a lot of agency to make things happen.
While this game maintains the same core as the earlier Tutankhamen, it differs in a number of ways. The artifact mix includes scarab rings that remove 1 point immediately when you collect them and remove 5 points from whoever has the most when all ten are claimed or removed. The ability to back up one tile is new as is the breaking of ties in favor of whoever is farther up the path. This latter detail is a clever brake on your desire to leap ahead and abandon tiles to others, although you can also use it as a tool to plan your moves and sometimes trap another player into losing a majority as they would need to overtake you to claim a tile in the set, but doing would put them ahead of you and make their conquest less valuable.
One change that's less than positive is the inclusion of five god powers, mostly because the gods are represented by images that read as nearly identical when viewed from a normal sitting position and they lack icons that remind you what they do. The game includes player aids that describe these powers in detail in an eensy font, and gameplay often sputters as one player after another tries to figure out which god can do what in the row of tiles before their boat. Games have a rich vocabulary of iconography that would summarize, say, swapping two tiles (tile icons with a double arrow between them) or placing a tile in the Underworld (a tile icon, an arrow, and flames), and it's disappointing to have unnecessarily herky-jerky gameplay due to a lack of that iconography.
On top of this, the god tiles were rarely chosen in our games compared to everything. I'd guess we averaged three god powers per game, but the potential of using them weighed on players' minds constantly, so we'd re-read what each of them does, then decide to do something else in the end. Having them in the game as a potential tool is valuable as a means of disrupting the straightforward choices of this artifact or that — but you want them to be easy to use whenever they actually are needed, akin to rear window wipers on a vehicle.
I talk more about this oversight and other graphic design issues, such as the numbing presence of gold on blue, while also comparing the features between Tutankhamen and Tutankhamun, in this overview video: