Suikoden has always been a series in which I have found empathy, between characters in the game, and between characters and myself. In the first one, when a pivotal character dies, the one who has always been with the character and would do anything for him, I find empathy and sympathy there. There is a similar situation in the fifth game. In the second, when a little girl witnesses the slaughter of her village, In Tactics where the young boy sees his father turned into a monster and then he dies. Seriously, it;s an empathy gold mine. In the first one where the dragon rider Futch loses his dragon, ad then finds a new one in the second game. We've all been through that. Also the main character in Summoner is one you can empathize with. Perhaps the characters in the first two Fable games. There are good examples out there. Just have to find them. Also, it wouldn't hurt if you wrote some of your own stories. Not necessarily designs, but narrative. What kind of situations would you empathize with? Not that you have to share them, but it might be a good exercise.

Empathy means relating to someone. You can feel for them because you've been in that situation, you know someone who is in that situation, or you've had some similar experience.

Death is one way to create empathy. It's probably the most common way to do it because many people have lost a loved one, and can therefore relate.

But that is not the only way relate to a character. When you see yourself in someone, you are more likely to empathize with him or her.

So if you've ever been homeless, you can relate with a character who's in that situation and trying to get on his feet again. If everyone around you has told you that you can't and won't succeed, you'll be able to find common ground with a character who no one believes in despite his potential. If you don't have much self-confidence, you'll empathize with a shy character. If you love sports, you'll find yourself rooting for that athletic member of the cast. Likewise if you play music, you'll be more likely to appreciate the musician.

Empathy can be found in practically any life experience shared with another. It hinges on familiarity and you feel like you can better understand someone who's been through the same things you have personally.That's really what it takes to establish that connection.

Empathy via putting the player in the place of the object/person they are supposed to have empathy for.

(even if its seeing a staged empathy of a character for something - to understand/recognize that 'empathy' the player has to be able to visualize it as from themselves)

Quick google search (10 seconds)

The latin root word for empathy is "pathos"

The Greek word pathos means "suffering," "experience," or "emotion." It was borrowed into English in the 16th century, and for English speakers, the term usually refers to the emotions produced by tragedy or a depiction of tragedy

I think empathy means the ability to connect with a character.

I really enjoyed XCom EU/EW and wasn't feeling it in XCom 2. In EW you start out in the "real world" and it smoothly transitions into science fiction which makes it easier to empathize with the characters because they're in our world and they are like us. If you're in science fiction from the start you need to work more to convince people that your characters are real and normal people.

Pretty simple formulae to it; to create empathy in the viewer make something express agency or emotion. Making your subject humanoid or giving it eyes helps a lot, but only because it helps the subject express what's going on in their pretend mind. The pixar lamp is a good example of motion expressing that the little lamp has a mind of it's own.

To create empathy you need to elicit the same emotion in the player as the game character. You do this by using all the tools you have at your disposal: art, music, game mechanics, writing etc. My favorite example is how Suikoden 2 made me empathize with the pixelated sprite that is the main character (spoilers):

Throughout the game whenever you rest at an Inn you are always waken up by your sister Nanami, who always says something cheerful to you. This happens so many times you start to take it for granted. At some point in the game Nanami dies and the fact that she is gone really hits home when you rest at an Inn and when you wake up you are no longer greeted by anyone, just silence. I've never seen the sense of loss communicated more effectively in a video game.