Amorim would have wanted Ruud to stay for a while though, like for example to get a report on who looks like how. Remember, this isn't a fifa or football manager game, players do not have ratings written on top of them, nothing is for certain and if nobody tells you anything, all you can base your assumption on is previous games, but that is based on another coach, and things are different now.
So if Ruud stayed, he could have given Amorim some insider information, that way Amorim could have started a bit better. In any case, I am sure that we are going to see him do fine, he will need just a few games adjustment period, and if he can achieve that, rest will be much easier for him to get better results on. When you are a new coach, the hardest part is to get to learn more about players, and their personality, sometimes takes as much as months but after you do learn more about them, you end up not getting anything worse, you end up only growing better.
Van Nistelrooy is not the only person who was in the team and knows everything that Amorim might need, so when coaches are fired they are allowed to leave the team the next day. Moreover, Amorim can get a lot of information by reviewing Manchester United games, he will already see the weak points. I don’t know what else valuable Van Nistelrooy can tell him that Amorim does not see.
Maybe he offered him to stay in the team, but it is clear that he could not give him a high position, as an assistant coach and Van Nistelrooy understands that it is better for him to get a head coach’s job in another team than to remain insignificant in Manchester United.