1) The Steipler Gaon (in the new printing of Kisvei Kehilos Yakov, Beitzah #174:12, page 314) writes that for the Dinim of Techumim it does not depend on whether the items have an owner or not. The crucial aspect is the fact that the item possesses importance. He writes that it is possible that this din is only mid'Rabanan.

It seems that according to Rebbi Yochanan ben Nuri (38b), who says that Cheftzei Hefker acquire Shevisah, we do not want items to be moved around on Shabbos a long way off from their original place. An item of importance should stay in its place on Shabbos regardless of whether there is an owner or not. This may be what the Gemara (38b) means when it says "even though it does not possess an owner, it is similar to it possessing an owner." Every item is important regarding Techumim, even though nobody owns it.

2) I found that the Beis Meir also writes, as the Steipler suggested, that the Din that Cheftzei Hefker have Shevisah, is only a Din d'Rabanan. This is in the Beis Meir to Orach Chaim #404, DH b'Reish Siman. He writes that certainly according to the opinion that they acqure Shevisah, this is only mid'Rabanan. So while the Steipler uses the word "Ulai" ("perhaps") the Beis Meir uses the word "Vadai" ("certainly") to express this Chidush. We can understand this to mean that Chazal wanted to give importance even to property which has no owners, and they said that it is considered as though the property does have owners and may not be moved too far on Shabbos.

3) However, on the other hand, I found also that the Divrei Yechezkel (7:12) cites the Chidushei ha'Ramban (Eruvin 47) that even for Cheftzei Hefker there are Techumin d'Oraisa. So according to this, we still have to understand why an ownerless object may not leave its place.

4) I found, bs'd, a different approach to this issue in Sha'arei Yosher by Rav Shimon Shkop zt"l. This is in Sha'ar 3, chapter 23, page 251 of the older edtions, column 1. He explains at length the Sugya in Beitzah 38b and writes that what Rebbi Yochanan ben Nuri said, proves "sheha'Chefetz Koneh Es ha'Makom" -- "the object acquires the place." Rav Shimon writes that if the object has an owner, the object acquires the same Shevisah as the owner, while if the object has no owner, "Koneh Es Mekomo" -- "it acquires its place."

5) Like anything that Rav Shimon Shkop wrote, one has to work hard to understand it, but one cannot avoid being reminded of the Gemara in Eruvin 17b, in a different context, ??? ???? ÷?? ?÷???, if one finds a dead body in a field, and there is nobody who seems to be responsible to bury the body, then the Halachah is that if it was buried where it was found, even though the owner of the field was not aware of the burial, one may not move the body from where it was buried because the dead body "acquired its place." There seems to be a similar idea, that according to Rebbi Yochanan ben Nuri, objects of Hefker "acquire" the place where they are located at the beginning of Shabbos, and they may not be moved more than 2000 Amos from there.

Dovid Bloom