Yes it can. The meaning of
zeigen can be, just like for
to show in English, that you explain something.
So if you are sitting in front of a map and give somebody the directions of a certain route, you could explain to another person what you are doing with
Ich zeige ihm die Strecke.
I would translate Strecke to route and Weg to path, so Strecke is more of a planned way to go somewhere. Like "I plan to take the route over the XY street." But just as in english, they are kind of interchangeable to a degree. Certain terms use a certain word though. Like "Ich gehe meinen eigenen Weg." or a racing track is a Strecke, not a Weg.
A road is a literal piece of soil on which vehicles travel; they often have a name (e.g. B302 or A5 would be typical names in Europe). A route can be a more abstract concept; it can be a plan of how you get from point A to point Z, potentially using several different roads.
"I guide him the route" isn't really proper English. I don't think guide can really have an indirect object. If you wanted to use the word guide, you could make "him" the direct object and say "I guide him to the route", or "I guide him on the route", maybe. Both of those have a bit of a different meaning and still seem kind of awkward to me, though.