The only reason for changing the story of the original book I can see is to make it interesting for people who actually read Christie's book. Well, in my opinion, such changes are actually very disappointing to readers familiar with Agatha Christie's works. I am one of such people and I was pissed at what creators of this episode did with the original.
I think brining the book on screen without any changes would have been much better. I mean, Agatha Christie is a very well known writer around the world, her books are masterpieces. And what is Tom MacRae, writer of this episode's script, known for? Writing a book for children.
Agatha Christie was a genius. At Bertram's Hotel is an excellent book with a powerful plot which is suited for the screen as it is. Why change it?