I'm trying to think of the name for this type of 2D engine...

Disclaimer: I am not a professional, I research, this is based on research, not professional opinion, when someone with more of a clue posts, listen to them not me.

Tiles are still used. Objects are broken into multiple sub-objects each of which is smaller than a tile.
http://www.metanetsoftware.com/technique.html
A tutorial can be found here.

For collision/efficiency purposes, tiles are best. Sure you can just collide everything with everything else, this type of engine is called either a 'kludge' or 'inefficient'. You can also collide linearly, but again, it's less efficient. I also have a design using 'cells' for collision (see matlab), but again, it's less efficient and the cells must be adjusted as objects move).

I think you should look into clip plane algorithms, bounding boxes, etc,

If you want to implement such an engine straight and ignore the tile suggestion, it may possibly be doable with an orthographic camera in Unity3d. Unless you mean vector graphics... which could still be done with polygons and clip-planes (to create tiles from vector graphics).

those are simply called 'sprites', so you're creating a 2d sprite engine, but ppl usually just call it 2d-engine. a 2d tile engine is a special version with the grid restriction you've mentioned.

to save yourself some time, I suggest to use some existing editor e.g. http://gleed2d.codeplex.com/

Call your engine something catchy, not a meaningless implementation detail.

Call your engine something catchy, not a meaningless implementation detail.

Actually, right now I am looking for the meaningless implementation details. A catchy name for the engine will have to come later.

My issue is that I know exactly what to do in a tile engine. A level in a tile engine has a level or world class that holds an array of tile layers and in each tile layer is a 2D array of integers, which are the tile ids for the tiles in the layer. Somewhere in there are the tile images and such. None of those names apply here.

those are simply called 'sprites', so you're creating a 2d sprite engine, but ppl usually just call it 2d-engine. a 2d tile engine is a special version with the grid restriction you've mentioned.
to save yourself some time, I suggest to use some existing editor e.g. http://gleed2d.codeplex.com/

No, not a sprite engine, although there will be sprites. I make a distinction between sprites and level objects. Sprites are reserved for the player, enemies, and other such objects. For instance, in a tank game, a sprite would be the tanks, projectiles, explosions and such, but not the buildings, roads, ground or other objects.

You may call it a 'Node'.
Node has a scale, rot, pos and many sprites.
May be even node children of its own.

http://en.wikipedia.org/wiki/Theatrical_property

No, not a sprite engine, although there will be sprites. I make a distinction between sprites and level objects. Sprites are reserved for the player, enemies, and other such objects. For instance, in a tank game, a sprite would be the tanks, projectiles, explosions and such, but not the buildings, roads, ground or other objects.

That's a meaningless distinction, and one that's not quite accurate against the historical context.

For this sort of construction, I have commonly used the terms "sprite map", "sprite layer map", "sorted sprite map", "sorted sprite hash map" and so forth. It's all irrelevant. What you name things in your own code and engine are irrelevant, as long as it is something that people can easily associate with what it is doing. If nothing else, go with the generic old "scene map" terminology. If people understand that yours is a 2D engine, then they will know all they really need to know if you just call it a scene. Name it something and get coding; if you feel like you have to change the name, well that's what search and replace is for.