A bit o'both, actually. Minis, for instance, are assumed for the rules (you play on a battlemat, everything refers to squares) and for the business model (accessories!)
The OP asked about computer use but to your question. Yes, I think it is pretty safe to say the 4e rules were designed with minis use in mind. With effort you can play with out but them but it does require a fair amount of DM hand waiving and/or behind the screen position tracking to make area effects work. This was a rules decision influenced by both a style of play that had come out of 3e and the business model that style of play created. WoTC didn't invent playing D&D with maps and minis but we certainly folded it more into the core that TSR had done.
More on the side of rules, though, since that's the part where it'll be experienced by the player. Does the DDI affect the way monster stat blocks are presented? (easily searchable, easily sortable) How about the way the Powers system works? (use-and-discard; cooldown times, etc.) Presumably, DDI stuff is as "core" as anything else, so would future books include references and rules that are usable without the DDI? A new Assassin Paragon Path, or a race book about the Revenant?
I don't think so. Those design decisions were made for ease of use in books. We wanted to get away from the text book feel some books had with massive multi-page stat blocks.
By design D&D Insider content is as core as something like Martial Power. I think those streams will remain somewhat exclusive (eg revenant lives on D&Di exclusively) as they did back when Dragon & Dungeon were in paper form. RTheer will also be content that lives on both as in the case of compendium or the Character Builder. That speaks to D&Di's nature as both content and tools/game aides.
I mean, those are kind of specific, but in general, I think the thrust of the question is: how much am I going to feel like I'm missing out if I don't have DDI? Will I feel like I'm going against the grain like I do if I don't have minis? Or will I feel like it's basically Dragon magazine, that it might be good to have, but it's an add-on, not a basic part of the game?
If the game was "designed with DDI in mind," then it implies that I'm missing out on a lot more than if "DDI is a tool to help you play D&D, not a thing you we're going to assume you need to play D&D" does.
If you catch the distinction? I dunno, it's probably a pretty subjective one, so I might be opaque as heck talking about this.
I guess you'll feel you are missing out as much as you may have felt in 3e if you didn't subscribe to the magazines, or play in RPGA to get campaign cards, etc. In the long run, I think the hard core 4e player (the one who who feels compelled to post on ENworld or own every book) will likely subscribe because it will be part of the game and playing culture of your peers.
Well, I did take your quote out of context to try and help illustrate my point. No worries, I don't think anyone who could enjoy a game of D&D would discount i
magnation!
Nice choice of colors. It makes me think of unicorns.