OK, I have good news.
Button for starting the game was greyed out because the game wasn't installed completely, I guess the earlier install process aborted abnormally because some of the game files were copied to the hd.
So, I launched AUTORUN.EXE from the CD through LocalE and pressing the second button (uhmm.. my Japanese is weak a bit 😀 ) launched the installation process. Now it completed normally, so the game launcher button became available.
It run but switching to fullscreen caused crash as shown on your video. It turned out that MCHASE.EXE has too small stack, that's the reason.
So I increased it to 16MB with EDITBIN and now the game runs in fullscreen too.
The only app compat needed for MCHASE.EXE is 8 bit color desktop mode, even Win95 is needless.
Also, I figured out what command line parameter is needed for MCHASE.EXE to avoid launching it from AUTORUN.EXE.
(I hope that parameter is not dynamically generated for each installation, so hopefully it'll work for you too.)
Patch: http://dege.fw.hu/temp/Magical_Chase_Stack_patch.zip
As for fullscreen mode: according to the proper game menu item, Alt-Enter should work to switch between windowed/full screen but it doesn't do. The only way to switch to fullscreen is choosing the menu item and there is no way back (quit can be done by Alt-F4).
dgVoodoo's built-in Alt-Enter support is also unusable because even when in fullscreen, the game thinks he is still in windowed mode so only the upper left region of the screen will be rendered. (Forcing a windowed app to fullscreen doesn't work if the game window is not resizeable.)
Altough it's not a problem for this game, I'm planning some modifications in dgVoodoo for taking the emulated desktop bitdepth into account when creating DDraw primary surface.