Yoche, your question is quite reasonable. When you get a chance visit the nasg.org website. All the S gauge standards are there including the ones for wheel gauges. I guarantee you it will be a pain to read and will not directly help with your engine. But it is good to know about the definitions and standards.
When Gilbert made these engines the only standard they followed was the width of the track between the railheads. The driver profiles do not follow the current S scale standards.
People who repair these engines as a business have either a spacer block that fits between the backs of the wheels or a jig that limits how far a wheel can be set on to an axle to get the correct wheel gauge with the Gilbert drivers. You can make a spacer block by cutting a piece of wood to fit between the known correct drivers on the engine.
While the wheel is off the engine check it to verify the white plastic insulator and the metal tire are firmly attached to the black center part of the driver wheel. The metal tires are known to come off of the white plastic insulators and then cause a short circuit when they touch the chassis. If they are loose a couple drops of thin superglue are used to reattach the metal tire to the white insulator.
S scale is 3/16" to the foot, so our models are 1/64 the size of the prototype in each linear dimension. Gauge is simply the distance between the railheads. Prototype standard gauge is 4’-8 1/2". S scale standard gauge track is then .883" to .905" between the rail heads for straight track.
The claim is often made that Department 56 ceramic buildings, of which I have many, are close to S scale, but even if they are they are not exactly prototypical.
Rich
I have heard that, too.
Great comment about Department 56. Many of the buildings in the Snow Village Collection are a close match for S scale. The Snow Village houses usually are too large but some are correct. The other Collections are different sizes.
Over the decades I have assembled a collection of around 100 of the Snow Village Collection buildings and houses for use on my Christmas layouts.
A few pictures.
They do look nice!
Those photos do look great. I have never attempted to place Dept 56 structures on my American Flyer layout, but maybe I should.
Rich
I think the Snow Village Collection buildings look great with Gilbert and other S scale trains.
Here are pictures of another small layout I made with Snow Village, this one used SHS track.
They look pretty good with O Gauge trains as well. Since the Dept. 56 collecting craze ended a few years ago I picked up a number of buildings at a VERY reasonable price. They’re not on the layout but come out once a year for under the Christmas tree.
I’m not sure if Dept. 56 intended their articles to be a good match with toy trains but it sure worked out that way.
Dept. 56 and Bachmann did intend for the On30 line of trains to be a good match for the buildings. That was the origin of the On30 line.
Not trying to confuse the OP with narrow gauge references here. 
Well, that would make sense…
I do need to keep an eye out for some of those Department 56 buildings. Maybe there’s something that would fit in on the Subdivision?
Interesting, I didn’t know that!
Good places to look for second-hand Department 56 buildings are antique malls and co-ops and thrift shops. OK, they’re not really antiques but a local a-mall is where I found mine and the most I paid for one was $35 for the Victoria Station.
Sometimes they show up at train shows as well.
Yeah, I’ve seen them there–just never the ones that I want!
I’m the reverse, until I saw them cheap I didn’t know I needed them! 
Oh, I haven’t considered getting any except when they’re cheap!