When running Dreamweb under ScummVM it applies keyboard commands just like @Japheth mentions in his "scummvm cheats" thread, but I think they go beyond just controlling the speed of the game.

In ScummVm you can go to Game settings and view the keyboard commands. One of them is pressing Esc for skipping and this allows you to skip Beckett's monologue at the very end of the game.

I don't think any keyboard commands are present when running in DOSBox so there is no way to skip the monologue.