That video was painful to watch. I don't know if I will be able to ever forget it. Filmed in 2013, but I don't know at which event/where.
In answer to your question, the R.E. didn't issue a sleeping mat. I am not aware of any army issuing a mat during the war. Ground cloths yes, but not mats (note: ground cloths, read poncho or shelter halves). I am not sure what you are referencing at 0:21 in the video; I didn't see anything wrapped over the right shoulder.
What is wrong with this individual's presentation of an Italian soldier in Russia:
1. Italy only had 10 divisions in Russia, not 25 (stated at the 0:22 mark).
2. Only one ammo pouch carried, not two (in 1GM they had two).
3. C.S.I.R. badge (not authorized until 1943 and not worn in Russia or by the R.E. R.S.I. yes). Ravenna wasn't part of the C.S.I.R., so unlikely any fanti would have been awarded the badge.
4. Should only be carrying the M39 borsa tattica, the M29 tascapane was for mounted troops (bersgalieri).
5. Gavetta should be inside the M39 borsa tattica.
6. No Italian decal on helmet (that was R.S.I.).
7. Khaki uniform is not summer, but uniformi coloniale. Not worn in Russia.
8. Wrong tunic for an enlisted soldier. Individual is wearing a sahariano ufficiale, not a soldato's camiciotti sahariana.
9. Wrong casco. Wearing a casco ufficiale, not a casco soldato.
10. Camo jacket was not issued or even autorized/made (1:22 in video)
11. Extra ammo pouch is actually the magazine carrier for a Breda 30 magazine. It is not an extra magazine, but used to carry the one authorized magazine when the Breda 30 was carried on the soldier's back or in the carrying case.
12. The casco on the table is actually a Wolseley helmet.
13. Fregio on the M33 tan helmet is wrong.
14. F.E.R.T. badge is wrong.
15. Ribbon on wearer's left is the 1GM campaign ribbon. Unlikely a caporale-maggiore would have served in 1GM. The ribbon on the wearer's right is unknown. It is similar to the Crimean War ribbon, but it lacks the red seen on the wearer's ribbon. It might not be Italian.
Some individuals posting in the comments made similar statements. An example of the problem with reenactors that don't do any research.
Pista! Jeff