I think things would have worked out similarly for Nintendo and Sega in the end, with Microsoft ultimately entering the console space with its "Direct X-box" anyway. However, some might say that Microsoft tends to copy the success of what others do, so would it have made a successful console without Sony entering first for them to follow by example? Let's just go with "yes" for this hypothetical.
First, I think Sega would have had another console after the Dreamcast, since that system, like the Saturn, would have done better. But with Microsoft's money to make very powerful systems to appease 3rd parties, the Xbox still would have ended up the place that games like Grand Theft Auto, Call of Duty and PC games found success on and made their home (plus, better online). Sega would not be able to compete on a financial level and, unfortunately, do not have neither the ingenuity nor the powerful IPs of Nintendo and would have bowed out after that.
Nintendo would have run into the same problem against Xbox that it did with Playstation so it would have ended up in the same place it is now. But with Xbox prone to poor leadership, it would have left the door open for another wealthy company to enter the fray as a challenger so it probably would not have remained a two-horse race for very long.
