Deer Gun and Youth Deer Seasons--Center fire rifles of .22 to .49 caliber and muzzleloading rifles of .45 caliber or larger are legal for deer. Center fire rifles of .50 caliber or larger using smokeless powder with a case length of greater than 3.5 inches are prohibited. Rifled slugs or patched round balls of 20 gauge or larger are legal for shotguns and muzzleloading shotguns.Minimum barrel length of shotguns is 18 inches. Handguns must have a minimum barrel length of 4 inches and be .35 cal. or larger. In addition, any center fire handgun designed to fire a legal rifle cartridge shall be legal. Muzzleloading handguns must be .50 caliber or larger. Fully automatic firearms, full-metal jacketed bullets, which are non-expanding, as well as altered projectiles are prohibited. All legal bow equipment as listed above in the Deer Bow season section shall be legal during the Deer Gun season. Crossbows are legal during the Deer Gun season with a Deer Gun or a Youth Deer license. Crossbows must: a) have a peak draw weight of at least 75 pounds, b) be equipped with a working safety to prevent accidental firing, c) have a stock at least 14 inches long, d) use bolts at least 14 inches in length.
* Use of night vision equipment, electronically enhanced light gathering optics or thermal imaging equipment for locating or hunting game is prohibited.
This is all directly from the proclamation. Looks to me like the Burris Scopes are perfectly legal.