Poirot to detect new generation online

They were good books. Leave them as books!

"Agatha Christie's classic plots translate beautifully onto mobile and internet platforms"

No they don't. They don't at all.

Look at the games charts at the moment (ELSPA). Do you see any murder mysteries there?
Computers have moved on from adventure games. This is mainly because they were rubbish. The biggest sellers and probably the best games are the ones that let you do what you want to do within a set environment.
You might find that there are murder mysteries within a game. For example, you could look at "Elder Scrolls: Oblivion" and call it a murder mystery. You'd be wrong though because it's a murder mystery where you can decide that you're bored with being a detective and go and fight demons with magic spells instead.
The whole point of Poirot, Marple et al was that it was a story. Stories are not interactive. They tell you what happens. Interactive games are all about you telling the system what happens and then seeing how the system responds.
Turning sports into games works well. Turning historical events into games also works well (what if situations). Stories into games don't work because you know what happens.