It's highly ambiguous, and intentionally so!
Now first of all, it is indeed strongly implied, even if never clearly stated, that this was Geralt. Among the obvious characteristics (his visuals, his horse, ...) and the ambiguous dialogue we also have the fact that he was hunting down one of Rissberg's "products", which the story already opened with and which he swore to hunt down.
However, even if that was Geralt, we should hesitate to draw a clear and definite statement about his survival or his prolonged aging from that. The entire encounter is highly ambiguous itself. You have to consider the whole surroundings of that encounter. Let's look at the matter:
There are very mystical and poetic statements about Geralt's place as a legend:
She didn't give up. "The Witcher will return from the afterlife! He will return to protect the humans when evil raises its head again. As long as there is dark witchers will be necessary. And the dark is still there after all!"
He was silent for long, looking to the side. Eventually he turned towards her. And smiled.
"The dark is still there", he confirmed. "Despite the achieved progress, which should, as they want us to believe, lighten the dark, eliminate the dangers and drive the fears away. So far the progress hasn't made any major success in this regard. So far the progress only talks us into believing that the dark is only a prejudice which darkens the light, and there's nothing to fear. But that isn't true. Because there will always, always be darkness. And always will the evil spread in the dark, always will there be teeth and claws, murder and blood in the dark. And always will witchers be necessary. And always shall they appear where they're needed. Where they're called. They shall appear when they're called, with sword in hand. With the sword whose brightness drives away the darkness, whose brilliance pierces through the dark. A nice fairy tale, isn't it? And it has a good ending, as every fairy tale should."
Now this could simply be him joking around about it, but it isn't placed in the text for nothing. It generally adds to the motif of a mythical fairy tale ending that the novel series already had afterall. (And like the novel series it presents us with that fairy tale-like ending while at the same time self-ironically pointing out, not to say mocking, that fact a little.)
Then there is the point of her possibly just dreaming it, when she awakes at the side of the street.
...The tale continues, the story never ends. But regarding the signs...There is one you don't know. It's called sun. Look at my palm."
She looked. "Illusion", she could still hear from somewhere. "Everything is illusion."
"Hey girl! Don't sleep, or they'll steal from you!"
She raised her head. Rubbed her eyes. And jumped up from the ground.
"Did I fall asleep? I was asleep?"
However, this is ambiguous, too, since she clearly awakes at the end of the forest. So she seems to have crossed the forest somehow. It's unclear if it only was Geralt's supposed sign that made her fall asleep and forget him. Yet this itself would still be rather unusual for him to do.
And last but not least, we also have the ambiguity of the novel series' ending and the unclarity about Geralt's fate.
And his possible afterlife in some mystical paradise (supposedly Avalon) in the first place.
All this reinforces that this epilogue isn't really intended to make a clear statement about Geralt's survival or his prolonged aging. Rather than that it follows the ambiguity, mysticism, and fairy tale-like character of the novel series' ending. And if anything, it seems to try to establish Geralt's fate as somewhat of a legend, a mythical hero, a ghost striving through the wilderness and protecting humans from monsters. But if he really is an actual ghost, or just a legend whispered and never seen by anyone, or the real Geralt returning into the world and living beyond his age, or if Nimue just dreamed all this, is a moot point. We just can't say and we're not really supposed to clearly say. You can and should decide that for yourself.
(In lack of an official English translation, let alone one I have at hand, the exceprts in this answer have been translated into English by me from Erik Simon's official German translation of Season of Storms.)