fwiw, there are many more Tekumel fans on the tekumel yahoogroup . The forums here are new, and many Tekumelheads haven't added them to their discussion efforts, at least not yet.
Like Dulahan, I'm very keen on good settings. Tekumel's cultural content is great, very distinct from the Medieval Euro-centric patterns that are common in many other games. The setting was invented by a linguist, and a full grammar and dictionary exist for the primary language, with grammars for several others too. That's just an aside, but the linguistic depth does add to the immersive feeling of the setting.
One of the things that the new corebook explicitly supports is different styles of play. You can play grim and gritty, with not much magic and lots of chances to screw up and get impaled, all the way up to running Heroes of the Age, saviors of the universe.
There is a stronger emphasis on social connections in Tekumel than there is in many other games. The society the game is set in is very collective. For most people, the clan they belong to is often more important than who they are as individuals. Temples and Legions are also major sources of social identity. Many character attributes relate to who the character knows, what relationships they have with them (e.g. Friends in High Places, or Nemesis), and traits that affect social interactions (Attractive, Archetypal, Teamwork). The Teamwork skill in particular is notable: it's part of the conflict resolution mechanism that allows members of a pre-established team to influence outcomes for each other in strong ways. Many npc's, from pack-hunting animals to the hosts of a high clan party may have Teamwork going for them.
You can run a traditional party of free-lance adventurers, but you'd probably end up bending the social patterns of the setting a little. Tekumel really isn't a good place for loner characters. More common is to have parties that have some basic thing in common. Often they are clan-cousins, or perhaps all serve in a particular Legion or at a particular Temple. The emphasis on social connection and loyalty to a larger group often stuctures adventures and outcomes. "Treasure" might be successfully defending the clan's interests (and earning the favor of the clan-elders), acquiring an ancient religious text that will bring prestige in the temple hierarchy, or ransoming captive enemy officers. With advancement comes material wealth too, but it is usually mediated through connections.
As to types of action, Tekumel has plenty of dungeons (with actual justification!) for the traditional dungeon crawl (e.g. Something's in the Clanhouse Basement, or Quest for the Lost Shrine of the 4th Aspect of Hru'u), but there're lots of other things to do too. Clans organize long-distance shipping by caravan or sail to distant empires and barbarian regions. The complex political scene makes for plenty of intrigue, and there are duels and gladiatorial bouts in the arenas.
Another good way to get a feel for things would be to look at some of the sample adventures. I particularly recommend Patrick Brady, Krista Donnelly, and Bob Dushay's work.
Look here:
http://www.tekumel.com/gaming_advideas.html
http://www.tekumel.com/vog01_02.html
http://www.tekumel.com/vog02_02.html
How's that for a start? More questions?