N64 pad was shown for years at that point, Sega's one was definitely an 'answer' to it, along with Nights, their Mario response.
Sega and Sony were essentially forced to graft sticks to their existing designs for backward compatibility, since their consoles did not launch with those controllers and a reconfigured pad for analogue control would not be popular since it would not work as easily/clearly with the games released to that point (eg see how N64 VC games' controls are mapped to the classic controller on Wii). For games that do not use the analogue, most people prefer the original pads since they are lighter have no sticks in the way. To this day Sony have the stupid symmetrical sticks because they were literally just grafted onto the original SNES style PS1 pad.
See my post *
here*.
I looked into this more and have a better timeline of the N64 controller -
1995
-July 31 "trust us, we have an unnamed source" website (IGOnline) posts a bunch of info about the N64 controller (mentions of this on usenet)
-Aug 13 Same website mocks up a sketch of it
-(around) late Oct, Nintendo.com releases prototype pic (first concrete info) advertising for Space World
-Nov 23 - full reveal at Space World
Even if somehow the Nights team got wind of a western website's unconfirmed/unsourced rumor (on the internet in 1995…), Yuji Naka's "...by Fall we had officially adopted the analogue controller you see today." heavily indicates no influence if he's being accurate.
Now add that Takahiro Hamano, a "Senior Programmer" on Nights, was also a programmer on Super Monaco GP II, a game that literally has a graphical representation of the XE-1 AP controller in-game along with analog support for it.
http://segaretro.org/Takahiro_Hamano
So you've got Sega supporting an analog thumbstick controller as late as 1995, that has striking similarities to the Saturn 3D controller (general/handle shape, analog/digital mode switch), and an important team member of Nights having had direct experience with it. Cmon now!
In my opinion, they 'lucked in' to having essentially hybrid SNES/N64 controllers for this reason. By coming in with mid-gen answers to the N64, they were forced to hedge their 2D/3D controller bets in a safer way than Nintendo had, and it turned out the compromise 2D/3D controller was semi-accidentally the best overall compromise.
Sony also lucked into dual analogue, it was added largely as an answer to Nintendo's forward thinking in inventing the stick (same with rumble "OMG we have DUAL shock it must be twice as good!" marketing bullet points etc), as well as having flight stick compatibility. But they clearly didn't have any idea what to do with the second stick most of the generation, Ape Escape used it for a bunch of gimmicks, most games ignored it, it wasn't until Alien Resurrection that someone used the N64 paradigm of two direction inputs for FPS on the console.
That last point also explains somewhat why Sega had one stick on the Dreamcast. Until 1998 nobody had made good use of the PS1 second stick at all, and the DC controller was designed specifically to be intelligible to new users, who were apparently confused by Saturn having so many buttons. Of course they could have looked at FPS games on N64 that used the d-pad/stick position or stick/c-buttons for dual input (or even Goldeneye which had the two controller dual analogue option), but FPS wasn't quite huge yet as Goldeneye only started taking off around the time the DC launched in Japan.
Where to start....
Sony revealed force feedback before Nintendo:
Sony dual analog (with rumble)
https://groups.google.com/forum/#!topic/rec.games.video.sony/zziF2Nxh5sE (next generation magazine #25 has an article on this mentioning the force feedback)
Nov 1-4 1996 reveal
April 25 1997 release
Rumble Pak
Nov 21-23 1996 reveal
April 27 1997 release
Sony's dual flightstick...
...obviously had nothing to do with the N64 (released months before) and already showed the value of two sticks for Sony. Or really, the value must have already been thought up because they released it in the first place.
The handheld version may have been a response to their competitor(s) analog controller, but to explain the second stick as a marketing ploy in light of the dual fligtstick...
Anyway, here are some pre-1998 releases using both sticks to move/aim simultaneously in different directions. That's the main purpose of having two, right?
Bonus Omega Boost (Polyphony Digital) demo... from
1995. Left stick move/strafe, right stick aim. But forward/back are inverted on the left stick.
http://zenade.angelfire.com/OB/OBD.html
Edit:
This is a random but fun thing -
Apparently the XE-1 AP worked with Star Cruiser (with analog), an actual polygonal 3D game for various Japanese computers (also had a Mega Drive version but no support). That game was made by people that would later work on Omega Boost here.
https://www.youtube.com/watch?v=sncAziTYZTs
...they also made Wibarm, a 3D free movement third person game in 1986 O.O