While there is no explicit evidence such as the ones you have mentioned that Re:Digitize takes place in the same universe as Digimon World, there are quite a few hints which heavily imply this:
- Here is one example that I can find right away, which is about the DigiTower. There are more implications, but this one is the one that really confirmed it for me. 
- The first sentence: 「ムゲンマウンテンのあった場所に突如として現れたデジタワーは…」, meaning The DigiTower suddenly appeared where Infinity Mountain used to be... Notice that no where else does Re:Digitize talks about Infinity Mountain, yet all of a sudden we have a reference of where Infinity Mountain USED to be. This pretty much implies that it is the same as an Infinity Mountain that we have dealt with in the past, and Digimon World would be the one that would fit this description best.
- Re:Digitize is also explicitly stated as the true successor of Digimon World, and on the site has also stated that 13 years has passed. The time passage of 13 years in the Real World, when converted to Digital World time, is a great amount of time as well (over 9000 Digi-years or 780 years), so anything that had happened in Digimon World can very well have been nothing but a mere unwritten legend for the Digimon.
- This would also explain the drastic changes in some of the environments of File Island, such as Gear Savannah being dried up into a wasteland, a volcano erupted out of Factorial Town so it is converted into a furnace, Beetle Land having developed into a city over time yet eventually was submerged, and the Dark Lord Mansion deteriorating into nothing but an underground waterway littered with furniture obviously belonging to a mansion.