Rolex Daytona? Need help.

[RolFX]

A few months ago my grandfather passed away and left me with this beautiful watch. Unfortunately, the box and paperwork for the watch could never be found.

It has a black face with "Daytona" written in red above the 12 hour cosmograph.

I've been trying to do some research to try and find more info on this watch, and have noticed something odd. The 60 second dial is on the left side of the face, which leads me to believe it is a 'zenith' movement watch. However, engraved on the band of the watch is '116520', was that not the new 'in house' style number? Also, my watch does not have a 'hour notch' at 12, 3, 6, or 9 O'clock positions. All of the watches I have seen online have small notches at the 3, 6 and 9 positions.

It does have the laser engraved Rolex insignia at the 6 oclock position.

Sorry for the low quality cell phone picture. I could not get a good shot showing the dials, but you can see where there are only a total of four glow in the dark notches. Did Rolex ever make a watch like this or is this most likely a replica?