Is there any problem with my games if I installed it under NTFS filesystem?

NTFS file system itself cannot cause problems to any software including games, because NTFS is just a way of data storage.

Software in Windows accesses files via upper-level Win32 API. Win32 API, in turn, redirects function calls to the drivers for the particular file system (NTFS/FAT/CDFS, etc.). Thus software, generally speaking, is not aware of file system it is installed on.

What could cause problems with games is Operating System itself. As long as Windows NT / 2000 / XP are more secure operating systems, and do not support 16-bit device drivers and real mode, some of games that work well under MS-DOS, Windows 95 / 98/ ME might not work under Windows NT / 2000 / XP.