Does anyone remember when games had instruction manuals?
Was that 'bad design' as they needed a manual to explain the basics of the game so you'd have some idea of what you're doing, rather than just opening up the game and interrupting even experienced players on new installs with an in-game tutorial where it spells out the bare basics for you?
Honestly, the latter is bad design IMO, the former is good design, just not the normal.
These days, most games are obvious. Especially to people like us who have played games before. We see a health bar and mana/stamina bar, we know what it means. We know that if we control a character from 1st or 3rd person, it'll be WASD to move in most cases. Birds eye view is click to do most things in most cases. I is for inventory, J is for quest journal, and M is for map. It becomes really obvious when you see new people playing the game though, that this isn't stuff that you can just 'know', and it does need to be spelled out for some people.
You could include a tutorial in game, however that'll annoy experienced players, and if you're trying to make the game immersive can be a bit weird. You can include the tutorial, but alongside the story and interwoven with it. Still annoying old players. Make it skippable and you still annoy old players, as they have the choice of having how to play the game spelled out to them, even though they know, or skipping some of the story.
I doubt this is what OP had in mind when he posed the question, but with games coming online through digitial distribution these days, there are no instruction manuals - the trusty aid that would explain to you how to play a game. Not only does this necessitate a tutorial, it necessitates a very long, in depth and complex, boring, tutorial for more complex games. Think of the civilization series. They simply have advisors instead of a tutorial, as if it were to sit there and spell out how to do everything to you, it would take an age, and you'd stop playing of boredom.
Another example would be Dwarf Fortress. You NEED the wiki to get into the game. I mean, you kind of don't, but you won't at all get what is going on if you don't use the wiki. It has no tutorial, as its still being made, and no instruction manual. Is it bad game design?
Not really. An instruction manual would be the best option for the game, rather than an in-game tutorial, and even with that you wouldn't really get how to play the game. You'd understand its basic mechanisms, but you probably wouldn't see how they all come together. That's not bad game design. The design of the game is good and accomplishes exactly what it sets out to... Or at least part of that so far. Its just a very different, in depth and complex game that isn't easy to pick up. Its got a hefty learning curve that never really slackens. Its very fun because of this though, and the things you can accomplish because of the game's complexity make up for its difficult barrier of entry.
So, it really depends on the game IMO. Sometimes yes, sometimes no, but in all likelihood the design flaw lies somewhere other than in you not being able to just play the game without needing to go through a manual of some sort, whether that be included with the game, or on an online wiki.