fairly sure A train was a maxis game and "A IV networks" was infrogrames ?
A train definatly had a dos version, dunno bout A4 networks might've been just windows

was wondering 2 things really.
1 how does GoG actually get authorisation to dosbox old games
2 any idea how long it'd take to get either A train or A4 networks if approved for dosboxing?

Same way it does for any kind of game. Find the rights holder, negotiate with them, get approval, package the game. Depends on current rights holder, and whether or not GOG sees those games as potential profit makers.

Both are japanese games from Artdink, and Japanese devs are not very DRM-Free friendly.

A-Train III (A-Train brought to western markets by Maxis) was MS-DOS game. Japanese version was re-release for Windows 95&98.
A IV Network$ or C.E.O. does seem to be MS-DOS game too.

But getting those here feels bit impossible. Probably best way to get your A-Train fix is to hunt it from ebay.