There´s a video game named "Star Traders: Frontiers" that I found to be the closest to an actual Traveller computer game since the ancient Megatraveller games.
You´re playing a Star Trader, the captain of an independent ship who´s making a living either by trading, by doing various missions, by exploring wilderness zones, patrolling your faction´s space, plundering and extorting merchants, or conducting espionage. The game takes place in a region of space settled by refugees from Earth several centuries ago; the various planets and space stations are each controlled by one of nine factions that are part of a constantly shifting network of alliances, rivalries and feuds. Each place you can do business at has its own laws, different goods it supplies or demands, and offers different degrees of various services.
One aspect of the game that I think translates very well to most Traveller settings is the Contacts mechanic. If you want to do anything but buying and selling whatever goods are legal at the current location, refuelling and repairing your ship and getting recreation and medical services for your crew, you need a contact for that. Contacts can be many kinds of important people, each of which offers a different set of services for you - a noble might offer you a trade permit (which you need for some of the more profitable but restricted goods) or a pardon (repairing your standing with their faction if you angered them), a smuggler may have rare trade goods and access to the black market, others offer recruits with special skill sets, discounts for services, a bounty hunter license or useful rumors, or they buy intelligence or scientific data. Almost all contacts also offer missions, which can take a wide range of shapes - simple "pick up and/or deliver", "acquire X amount of good Y and bring to place Z", transporting a passengers, catching or killing a wanted criminal, espionage, exploration...
And before you can work with a contact, you need to be introduced to them; you start out the game with a few contacts, you can get your contacts to introduce you to their friends and allies, there are certain crew talents that give you a chance to gain a new contact (such as through a meeting in a spaceport lounge, or during business transactions), and once you´ve gained some fame, you will occasionally be approached by VIPs on their own initiative. It really gives you the feeling that you are initially an outsider to the world of the rich and powerful who is slowly being introduced to these circles due to their actions and exploits.
The game system, unfortunately, isn´t even remotely like Traveller. Each character (your captain, officers and crew) have a class and level, with a fixed skill set - e.g. every level 5 Merchant has Negotiate-5, Command-3 and Tactics-2. Every couple of levels, they also get a talent. Some talents give you special options during combat or exploration or espionage, others grant you a certain chance that something positive happens in certain situations or just plain make it happen (such as a chance equal to the character´s Negotiate skill to learn a new rumor while conducting trade, or automatic reduced jump fuel usage equal to the Navigate skill). Some, which I find particularly useful, trigger automatically when you fail a skill check, turning it into a success. All such talents have a cooldown of anywhere from three weeks to half a year, limiting their use and preventing them from being automatic "get out of jail free" cards that mean you don´t need skilled crew any more.
FWIW, I can really see some of these talents being adapted to Traveller versions that use traits the way Sword of Cepheus does.
Combat is fairly abstracted, just two ships, or two groups of crew members, facing each other and taking turns attacking; IMHO it is not one of the game´s strong points.
The graphics are relatively simple, but they work. Sound effects are fairly rudimentary - engine sound while travelling, weapons sounds in combat, a warning ping when you fail a skill check, stuff like that.
The game´s great strength, IMHO, is in the atmosphere it creates, and in how it allows you to travel this universe and interact with it in any way you choose - you can be a trader, an explorer, a diplomat, a spy, a bounty hunter (or assassin, the distinction can be vague at times), a smuggler, a pirate... There´s a main storyline divided into several acts or "Eras", which you can either participate in or completely ignore; the story will progress without you after a while even if you yourself never do anything to move it forward.
The game also comes with a 35 page lore book detailing the universe - a universe that could really be (and *should* really be, if not for the matter of copyright) a Traveller setting. And it´s also still being explanded after four years, if rather slowly.
Space isn't remote at all. It's only an hour's drive away if your car could go straight upwards. Sir Frederick Hoyle
Earth is the cradle of humanity, but one cannot live in a cradle forever. Konstantin Tsiolkovsky
Man has earned the right to hold this planet against all comers, by virtue of occasionally producing someone completely bat**** insane. xkcd #556
Just like people, stars can be very important without being terribly bright. Phil Plait, "Bad Astronomy"