I think Vintage is a competetive format in general.
Its not solved, its constantly evolving, the play patterns are very skill testing in ways that are not common in other formats. What i very much like about Vintage is that often every small little mistake or misjudgement can lose you the game on the spot. In other formats, while this can certainly also happen, especially against combo decks, it is not nearly as common, and most small mistakes just lose you value or tempo. (which ofcourse might lose you the game down the line, but rarely immediatly). For the record: Iam not trying to say that other formats are less skill intensive, it is just different kind of skills that are commonly used in Vintage.
It is also not an easy format to get into, especially for new players. Most new players can easily pick up limited, standard or even modern. Not so much with the older formats, and while price and exposure play a role in that for sure, i think it is just hard for new players to grasp the huge amount of mechanics, legal sets and cards as well as play patterns and rules (a lot of strange triggers, interaction on the stack, stacking of abilites...). The format also really rewards experience. For those reasons i believe Vintage is very well suited as a competetive format.
Why then does it feel so relaxed? I think its a number of reasons:
Some players still think that Vintage is more luck based than other formats ("whoever begins wins on turn 1", "hey had the force, they just got lucky", ...) and i think this stigma is just plain wrong. Ive been playing standard for a while now just because i can play it for free on mtgA and there are many many games that feel to me, that it was just luck based and as a control deck player i often feel 'bullshitted' when my opponent begins and plays threads ahead of the curve before i have enough mana for countermagic. This feeling might just be because i dont understand the format enough (however iam not really interested in it enough to do so). If i play older formats like Legacy and Vintage i very rarely feel like it, one one hand because you have cheap and even manaless interaction and on the other hand because i think i understand and know the format way better and can predict when a turn might get very explosive, what too look for and how to play around it. (at least thats what iam telling myself, in reality i dont even own power...scub). I think understanding a format and variance greatly reduces the feeling of "i just got unlucky, its just a coin toss".
The next reason might be the lack of pro or semi pro interest to up the average competition because of the lack of regular high level tournaments and WotC support. This got a bit better with the introduction of the format points of mtgo and look how a great player like Nassif ran through the field (iam aware this might just be a statistical anomaly, but it is impressive for sure) . Pro(-team) interest would probably also speed up the evolution of the format, if that is a good thing everybody has to decide for themselves.
The next reason is i think is very positive in my opinion, but still contributes to an over all more casual feel: The player base of Vintage is much older compared to other formats. What does that mean? Players that, while still definetly wanting to win and beeing very good, tend to be less spiky. Most players dont throw fits or get overly salty when they lose (something that is very commonplace in standard and modern). I think the Vintage playerbase is just more level headed, mature, releaxed and way less toxic than the average Standard or Modern player. Players are more trusting and know how to have a fun night, while still playing competetive and highly skill intensive Magic. That attitude might seem less caring, but in my experience people care about this format a whole lot, they just dont scream and kick to make their voices heard like it is sometimes commonplace in other formats (Well, at least not outside a B&R or Reserved List thread )
Toxicity does not equal competetivenes per se!
In summary Vintage as a format is potentially competetive and very skill intensive, but the players tend to radiate a more relaxed attitude, and some misconceptions make the format seem like something it really isnt.
Thats just my thoughts about it.