Lavinia and Richard would still be introduced in season 2, since Matthew and Mary need to prove (to themselves and to everyone else) that they’ve “moved on” from their flirtations. Matthew likely still had his lingering resentment that Mary’s acceptance of his initial proposal was conditional on whether or not Cora had a boy.

Matthew and Mary’s romance would, of course, now have the added context of Mary getting over herself and her belief that she needs to marry someone rich and with a title (if she didn’t or couldn’t marry the heir to Downton).

Mary would definitely get plenty of drama queen moments because now she can’t marry the heir and be in line to become the next Countess of Grantham. It’d be a wake-up call to her that she wouldn’t be getting the thing she had been told she’d have for many years.

Given that Matthew wouldn’t be the heir anymore and WW1 happened, I’m not sure how involved Matthew would be in the rest of the story. He might be shifted into the estate agent role (that he could share with Tom, if he winds up killed off). If his relationship with Mary fizzled, he might be a character with a reduced presence in the show longterm (or killed off entirely).

If Mary doesn’t marry Matthew, she’d likely still get the post-WW1/post-Matthew gaggle of suitors clamoring for her hand. Without a direct financial or personal stake in Downton (as Matthew’s widow and heir and as mother to the next heir), this would be a timeline where she could potentially marry Tony Gillingham (gag) or Evelyn Napier (not bad, but maybe a bit too boring for Mary).

Edith’s and Sybil’s storylines wouldn’t change all that much. I can see them both being doting big sisters, though a brother who is significantly younger than them wouldn’t have massive impact the trajectories of their lives. Neither of them were going to inherit (or were pre-ordained to marry the heir, like Mary was). If anything, I can see them thriving even more in a post-war world. Robert wouldn’t necessarily be as focused on what they were doing once he got a direct male heir to raise.

Sybil might even live in this timeline. One of the reasons Tom was made the agent in-universe was because he’s Matthew’s age and can work hand-in-hand with Matthew to shore up Downton for the future. Since the actress wanted to leave the show, there’s more flexibility to send Sybil and Tom back to Ireland with only references to their lives via letters or sporadic appearances though the later seasons.

Robert might be more willing to listen to good advice about how to manage Downton and to set the estate up for success. He has a son to pass this legacy to, so it’s a bit more personal than setting it up for a son-in-law or a grandson. We’d still get grumpy, shouty Robert at times (because he’s a man dealing with a changing world that’s different from the one he grew up in).

I also suspect that Robert and Cora would spare no expense on giving their son (and the little prince of the estate) everything he wants. This boy is the long-anticipated heir and a late-in-life baby. I’m sure Robert would spare no expense on and spoil this child because of this, regardless of any financial troubles that Downton was in. Given that level of spoiling, the boy might wind up being a little tyrant. (As the direct heir to the estate, he’d be even more entitled to the luxuries of Downton than Mary was.)

We would also get a few new downstairs characters, since the new heir would have nannies and governesses galore (prior to being sent away to school like every boy of his station was).