Does all surface runoff move directly into rivers, lakes, and oceans? Explain.?

No. A great deal of it evaporates. For example, the Great Lakes actually makes it's own weather by evaporated moisture from the lake itself. And evaporation from oceans are what keeps the moisture moving across land in form of rain cloud. There is estimated to be 300 square miles of water in the earth's atmosphere at any given time in the form of rain, snow, sleet, clouds, fog, etc.

by definition "surface runoff" means it runs off the soil. If not into rivers, lakes and oceans, where do you think it will go.

A very large part will go into the ground and move slowly under the ground.  Yet it too must eventually emerge into rivers lakes and oceans as the lowest point at which it can emerge.  Quite a lot is evaporated in situ.  So only a small part of the water moves directly as surface runoff.

If it's runoff then it is water that has not infiltrated (soaked into) the ground. Some at least will evaporate and some will collect in puddles and never reach rivers, lakes, and oceans.

Not usually.  It can if the surface is totally impermeable, but that is extremely unusual.  If there is open space in the ground, even tiny open space, some of the surface runoff will fall into it, and as long as the open space connects to other open space, some of that water will make it downhill by passing through the underground. Around here where I live, it is pretty common to encounter the water table at somewhere around 1-2 m below surface, sometimes as much as several meters, depending on the situation.  But it is always there.  Some of the runoff always bleeds into the ground instead of making it all the way to a surface water body.  Just a matter of what proportion.

The question is a bit vague or too specific, I cannot tell which, because the term "surface runoff" could be taken to mean any water which does not infiltrate, and does not evaporate, and thus excludes any portion of some of the runoff which might evaporate or sink into the ground even if spending part of the trip on the surface, and thus it must all end up at some surface water body eventually.

If water stays as surface runoff the entire distance, it will end up in a waterbody.  But that is pretty well defining the term "surface runoff" as water which travels all the way to a waterbody without some diversion through a different route, so the answer is defined as yes.  If you use the term to mean water which runs overland the entire way until reaching a water body, it definitely will be water that does exactly that or the term won't apply and you wouldn't call it that.

But to answer, not all surface runoff stays on the surface all the way and so becomes not-surface runoff.

Not directly, some ends up in underground aquifers.  Some is diverted along the way and used to irrigate crops or provide water to communities.

I find it sad that kids today can't even bother to do a bit of reading about how the world they live in actually works.

No.

Because "all" and "directly" usually mean the answer is no.

Or more to the point of your question, because some of it doesn't.

Some of it is collected intentionally, some of it soaks back down into groundwater, some is evaporated before it gets to a body of water, etc.  And even the parts that make it to those bodies of water generally do so indirectly via much smaller channels than rivers.

Certainly some does, but most surface runoff moves into streams and rivers that then carry that runoff to lakes or to the ocean, so must runoff doesn't go directly into lakes and the ocean but into lakes and the ocean indirectly via streams and rivers. Lakes themselves can then also feed rivers that sends that runoff ultimately to the ocean.

Here's an example: It rains in Grand Rapids, Michigan. Runoff from that rainfall ends up in the Grand River. The Grand River then empties it into Lake Michigan. Lake Michigan then empties it into Lake Huron via the Straits of Mackinac. Lake Huron then empties it into the Clair River. The Clair River then empties it into Lake St. Clair. Lake St. Clair then empties it into the Detroit River. The Detroit River then empties it into Lake Erie. Lake Erie then empties it into the Niagara River. The Niagara River then empties it into Lake Ontario. Lake Ontario then empties it into the St. Lawrence River. The St. Lawrence River then empties it into the Atlantic Ocean via the Gulf of St. Lawrence.