There is a hurdle and jump drive does define Traveller
Communications lag is an inherent part of the game and jump drive creates that. Jump was part of the before the aliens you list. Jump was part of the game before the 3I and the Emperor. Jump was there from the beginning.
Jump is an inherent part of the ENVIRONMENT within which the game partakes, but it's not necessarily a first class concept during actual gaming.
I mean, I get it, I understand. Traveller implies traveling, and traveling means Jump. The society is structured around time lag. That's why it's feudal in nature, why it strives on self-governance, etc. Certainly a core, fundamental element of the background.
However, how many scenarios and adventures actually require Jump? Once you Somehow(tm) (whether by jump, train, air/raft, or donkey) arrive at Adventure Spot 2A, to partake in Adventure, Adventure happens.
Jump, subsectors, Dukes, the 3I, etc. Those enrobe and provide context to the adventures, but aren't (usually) first class items within the adventures themselves.
How many published adventures actually involve Jump? How many Amber Zones?
How many folks going to a convention to "play traveller" actually end up in Jump space?
I'm guessing not many.
Comm lag is why trade works the way it does. Comm lag is why interstellar governments work the way they do. Comm lag is why you can't send for help and why the people on the spot must tackle any problems. Comm lag is why adventures happen the way they do.
But all of that can be abstracted away. There's nothing stopping different worlds in a game from having different prices and such, imperfect information, imperfect markets, "manifest" through "jump". (Mind in a actual game, keeping something like pricing information unavailable to players who will route around ANY lag [jump or otherwise] is nigh impossible. The Internet Knows All.)
All of those limitations of jump can be expressed through narrative without actual mechanics in game. Sure you can still Jump from world to world, but, that's all it does "jump". Just like you can have "Orders from the Duke" who lives in the "Palace" that happens to be a closed off building no one can enter. You can still have a Duke and never see him.
But you're not going to be able to let Timmy play Traveller MMO, be on Regina, and chat out to his friend to come log in and play, and find his friend is 4 jumps away. "Sorry Timmy, I can't come and play, I won't be able to get their until next month, or, next day, or 4 hours from now.". As I said, WoW has travel, and back in the day it could take about 15 minutes to get from anywhere, to anywhere. While not "instant", it's much faster now.
In a single player game, Jump is easy to do. You have some outside constraint that's affected by time. You burn a week in Jump, and thus those constraints have more and more impact. But in clock time, you burned 5 seconds by clicking on the Jump button, watching a pretty display, and then arriving at your new locations.
Star Raiders, long ago, on the Atari did that really well. You had "Hyperspace" to go from sector to sector. If you "jumped" from one end of the map to the other, yea, you'd be in Hyperspace for a few seconds compared to if you just jumped next door. Long enough to make you feel you traveled farther, but a minor affect on actual play time.
But in an MMO, real time, calendar time, clock time, PLAYER time, is what's important. Not mythical game time, no matter how fundamental to the background it is.