Defining what makes a SEGA game a SEGA game has always been complicated. I'm sorry, but "it has blue skies" or "its arcadey" or "it was developed internally" doesn't cut it. Is "Rise of Nightmares" less of a SEGA game because it doesn't have poppy music or blue skies? Nope! Is Ecco the Dolphin less of a SEGA game than Sonic because it was second party? Not in my book.
Really, like ROJM laid out, it all boils down to categories:
First party games - original IPs
SEGA games developed by internal talent for the arcades and console systems, featuring original IPs.
Examples: Sonic The Hedgehog, Shenmue, Jet Set Radio, Virtua Fighter, OutRun, Rhythm Thief, Viking: Battle for Asgard
First party games - acquired IPs
SEGA games developed by internal talent acquired by SEGA for the arcades and console systems, featuring IPs that originated with the developer before their acquisition by SEGA.
Examples: Total War, Football Manager, Spiral Knights (a rare case of a third party game becoming a first party game)
First party games - licensed IPs
SEGA games developed by internal talent for the arcades and console systems, featuring licensed IPs.
Examples: Dick Tracy, QuackShot, Castle of Illusion, Astro Boy, Alien: Isolation
Second party games - original IPs
Games made specifically for SEGA by other game studios, SEGA retains the rights to the IPs.
Examples: Ecco the Dolphin, ToeJam & Earl, Bayonetta, Vanquish, MadWorld
Second party games - licensed IPs
Games made specifically for SEGA by other game studios, featuring licensed IPs.
Examples: Ghostbusters, The Golden Compass, Aliens: Colonial Marines, Thor: God of Thunder
Third Party aka SEGA published
A game made by another studio or company/publisher that gets SEGA to publish the games for them while the game dev still retains the rights.
Examples: Heroki (still unpublished), Jack Lumber
SEGA as a third party
This is a situation that I don't think gets much attention, basically games or characters that SEGA licenses out for other publishers to use. Examples would be Sonic in Super Smash Bros. and Bayonetta 2.
In the case of Sonic in Super Smash Bros, he is an original SEGA IP being licensed to Nintendo for use as a cameo. Bayonetta 2, meanwhile, is a Second Party original IP licensed to Nintendo. It's a rare instance, as most of SEGA's second party content is not all that popular enough to warrant another publisher wanting to release a new game. Remember that Ecco's creator pitched an Ecco iOS game that SEGA turned down. Seems that the concept didn't catch any other publisher's eyes either, as the game ended up being a non-Ecco title that hit Kickstarter and failed to be funded.
If we see a Shenmue III, I could see it being a third party title that SEGA licenses out.
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So really, it all depends on your preferences.
My preferences? I can agree that stuff in the Second Party Licensed IPs and Third Party published categories really have very little connection to SEGA outside of licensing/publishing deals. Still, I'll cover them for SEGAbits and treat them as SEGA games, but I personally wouldn't classify them as "true SEGA games". I say "true SEGA games" in that SEGA did not develop the games internally or even assist in the development of a second party IP that they, in turn, own. Also, I put "true SEGA games" in quotes because at the end of the day even those games are SEGA games, despite the lack of internal connection to the talent (that SEGA DNA, if you will).
There are, of course, exceptions. Ghostbusters, for example, is credited as being developed by Compile and SEGA. The game was also built for SEGA hardware. So despite the second party publisher, Compile did have strong ties with SEGA at the time, and the game itself had input from SEGA and is a Genesis title. So I would say that Ghostbusters is more of a SEGA game than, say, Aliens: Colonial Marines. It all depends on how hands on SEGA themselves are, and in the case of Aliens: CM I feel they were very hands off.
I disagree with those who brush off a game like Viking: Battle for Asgard as not being a SEGA game because the developer was acquired and the team doesn't have some magical SEGA DNA. They're now SEGA staff and are just as much an internal team as Sonic Team or AM2. So an original IP from them within SEGA is just as much a first party title as Sonic or Virtua Fighter.