I assume the Miniart railroad set was for WW2 Germany, but the same gauge must have been used in the parts of Europe that Germany conquered, since the Third Reich did much railroad expansion during its existence? And the gauge would remain standard after the war where the Germans set foot?

Not sure of your question, but the 'German' gauge you refer too was the standard gauge throughout Europe even before WWII. All Europe was and is on a common gauge so a train can go from the UK via a train ship to France and then right across the rest of Europe, stopping at the Russian border.
The Russians had (may be wrong but still have?) their own different gauge.

The general "standard" gauge for Europe and the US is 4 feet, 8 1/2 inches as originally determined by the official wheel spacing of Roman chariots.

The Russians went to 5 foot gauge specifically to make it difficult or impossible for invaders to utilize the Russian railroads for supply. In WWII the Germans spent considerable time and energy re-gauging many of the Russian tracks to improve their supply lines.

There are other, narrower gauges used at various places around the world, usually in extremely mountainous terrane or to save on initial construction costs; 36 inch, meter gauge, 30 inch, 2 foot gauge and 18 inch.

Narrow gauge, because it can negotiate tighter turns, is also widely used in industrial applications, including mining and sugar cane or banana plantations.

George Stephenson's 1435mm gauge eventually won the "War of the Gauges" in England against Isambard Brunel's 2140mm gauge, and other countries importing their rolling stock would lay track that fit their purchases. Britain converted all the broad-gauge track of the GWR and connecting lines to standard gauge to eliminate slowdowns from having to transship cargoes between the two rail nets. In British colonies in Africa, though, 3'6" gauge was the standard, and regauging to standard gauge is ongoing as tracks are renovated.

Russia wasn't the only country to deliberately pick a different gauge as a defensive maneuver; Iberian gauge (1668mm) was picked by Spain and Portugal for this purpose, and Canada's railways were originally 5'6" gauge to prevent their use by US rolling stock. Finland uses a 1522mm gauge, which is interoperable with Russian broad gauge, although Finland has different structure and loading gauges (how much room around the track needs to be reserved, and how big railcars and cargo can be, respectively) are different, which can lead to problem with tunnels.

Because of the advantages in load capacity it offers, India adopted a 1676mm broad gauge, and is in the process of converting its narrow-gauge lines to that gauge, although some metro rail projects use standard gauge.

Ireland also uses a broad gauge, 1600mm. Its first railroad was built as standard gauge, with two others built to different gauges. When standardized in 1843, 1600mm was picked because none of the railroads used it, imposing an equal burden on each railroad to change over.

Track gauges in the US were similarly divergent, because railroad operators didn't plan for interoperability. B&O and Boston&Albany used standard gauge; the Erie and Lackawanna railroads used a 6' gauge, Pennsylvania used 4'9", almost standard gauge; the South had a collection of broad gauges, with 5' being the most common, and Canadian railways used 5'6" as a deliberate choice, like Russia and Spain before her, to make its rail lines incompatible with US rolling stock.

The Transcontinental Railway was originally intended to be laid with the 5' gauge of California railroads before Lincoln determined to make it standard-gauge to match Eastern railroads; this cemented standard gauge for American railroads, and all track was eventually relaid to this gauge, converting what had been some 20 different rail gauges to a single standard.

That the standard gauge derives directly from Roman chariots, though, is anecdotal at best. The north England tramways, from which Stephenson had taken his track gauge, had somewhat arbitrarily picked five feet as an overall track width, using rails two inches wide, making a gauge of 4.8"; Stephenson took that gauge, but later widened it by a half inch to give more room for the wheel flanges. The rutways at Pompeii and Herculaneum have track widths of about 4'9", with an inner gauge of about 4'6" -- close to, but different enough from Stephenson's gauge to be an amusing similarity due to a common constraint, since both the Roman chariot and the wagons of the English tramways needed to be about the same width to be drawn readily by a side-by-side team of horses. That width isn't cast in concrete, though -- for example, the standard design for Conestoga wagons had a wheel track of 5'4".