Kirito has made it clear that his future lies in virtual reality, especially in the final episode of Sword Art Online: Alicization-- War of the Underworld. Not only does he want to study electrical engineering in college, he means to someday get a job working for Rath. That is, of course, unless his parents have something to say about it.
It seems like Kirito's parents could stand to be a little more averse to Kirito's heavy investment in VR. After all, it's led him into dangerous situations and even hospitalized him several times. This is to say nothing of how more people seem to know him by his in-game name than his real name. Their main concern is their boy's happiness, as is the case with any good parent, but that might require a firmer stance regarding where he plans to go in life.
All of this depends on exactly what Kirito's plan for the future is. He originally stated he wanted to study electrical engineering at a college in America. He has since changed his objective to studying in Japan, namely at the Toto Institute for Technology. He hopes that this course change will help him earn a job at Rath, or, as the general public knows it, the Oceanic Resource Exploration & Research Institute.
Upon hearing this, Alice rushed to Kirito's defense, certain that his parents would reject his decision. She cited her own disagreement with her father about becoming a knight, a choice she's convinced he eventually learned to understand. She also made a point of how Kirito was a hero in the Underworld. She seemed certain she needed to say whatever she'd have to in order for Kirito's parents to try and understand their son's side of the argument.
However, Kirito's parents were much more agreeable than they let on. For one thing, they already acknowledge their son as a hero, namely the Black Swordsman. More importantly, they showed their full support for Kirito, pursuing his academic and occupational goals fervently. Their only real stipulation was that their boy lives his life without regret.
With all that said, however, Kirito's parents should probably be a little more wary of electronics, especially VR, given all of their son's past experiences. He's essentially had to deal with a mad scientist, rapists, murderers, and even a paramilitary group, all because of VR. He also may have to deal with a rogue AI copy of himself in the near future. Granted, many of those situations were beyond his control, but there were definitely times when he placed himself in danger he could have backed out of. Even if he somehow never encountered such a perilous situation ever again, that reckless approach to life would concern any parent.
As for how Kirito's parents really feel about these past VR-related incidents, they're probably not too concerned, nor should they be. They seem smart enough to recognize just how many of these incidents were beyond Kirito's control. They also likely know better than to blame VR directly for Kirito's problems; it was the instrument for the incidents, not the direct cause. They may also recognize Kirito as capable of handling himself in these incidents, even if they pray it never comes to that. With all that in mind, letting Kirito invest his time into VR doesn't seem like such a bad idea.
It's also important to let Kirito pursue electrical engineering because of how much time he's invested in it. It's clear that this is something he both knows a lot about and is passionate about. If he cares that much about this field and he can make money doing it, that makes things all the better. In this regard, Kirito's parents should be in support of their son's decision.
As for living without regret, that likely pertains to Kirito living life to the fullest. His parents would want to be sure that he knows how to focus on improving his real-world self as well as his virtual-world self. As long as he leads a morally upright and fulfilling life with equally good people he can count on, his parents should have nothing to worry about.
As hands-off as Mr. and Mrs. Kirigaya's approach to parenting is, it seems to be working. They support Kirito's pursuits and ambitions and trust that he'll make the right decisions in life, including with regard to VR. This may have led him down some dangerous paths, but he apparently has both a good enough head on his shoulders and good friends to help him through them. If he decides to pursue a career in VR, his parents should have plenty of reasons to stand behind him.