Protected mode was a way to get around the old DOS limitations on memory. In DOS, there was the base 640K of memory, the other 384K up to 1MB was considered the system area, and then any memory beyond that was accessed either as EMS, which pages the memory into the system area in 64K chunks, or XMS which accessed the memory directly...the catch is you had to load different TSRs to access this memory and your programs had to be limited to going through those.
The thing protected memory did was to make all that memory available in one chunk, like the base memory is all the free memory in the machine...the catch is it involved several new functions, which DOSBox happens to not support right now. Any application can usually use protected mode, if I recall right, but as a key thing for games usually a file called DOS4GW.EXE is present.
Bottom line though, is you won't be running this game until the DOSBox coders support protected mode.