I guess nobody else is going to take a swipe at answering this, so I'll give it a shot.
Will the desk bow in any way?
Depends on load and construction details. With the items pictured, even a pretty lightly constructed one will probably not bow/bend/sag much, and there are ways to frame it so that a much heavier load could be supported. What you need to do depends on what you anticipate possibly happening to the desk - if people might sit on it, it needs a good deal more support than if it's just holding a modern lightweight computer and sundries. But if you might set a box of papaer or books on it, then it needs more again...
Is it too wide?
No, subject to adequate framing.
Will the frame suggested be sufficient?
Color me dubious on that front. While it's sufficient for the purposes it was built for (evidently) it's more fully supported than what you are proposing to do, which allows it to be not so robust - but again, this is also load dependent, though having the desk break IF someone sits on it (even if you don't intend it to be used that way) can be somewhat annoying.
Does any one have any other thoughts?
Stressed skin panel construction offers some interesting possibilities, depending what you are up for, and what you are looking for.
How will I attach it to the walls?
Multiple options. Ledger boards on each end are a good approach if you don't mind them being visible. File cabinets and no wall attachment as with the linked plans are another approach, but evidently not what you want. Huge shelf brackets as you mentioned in a comment are another option. Much of this comes down to YOUR concept of a "floating" desk or how important it is that the desk slab appears to be sitting there with "no visible means of support" and whether that means "nothing visible when standing 6 feet away" or "nothing visible when lying on the floor."
In the "can be effectively invisible" line, you attach angle iron to the side walls, build a thick-ish (you can thin the front edge) slab, cut slits in the ends that slide over the angle irons and slide it in place. That calls for some precision crafting. The slab needs to be thick-ish both so that you can have a non-contributing part below the angle iron to conceal it, and so it's stiff enough to span 2 meters while only being supported at the extreme ends.
Less drastically austere solutions allow for a cross-beam below the desk surface but beyond/above where your knees would hit it, and visible supports on the end walls that the desk slab sets on top of.
The giant shelf bracket approach is arguably "not really floating" but does have no "feet" or "legs" down to the floor.
All will hold the desk slab up. Different ones require more or less structure from the desk slab itself, due to greater or lesser spacing between support elements.