I've never seen this map before but it's odd when you think about what it covers. At the time it would cut off U.S. access overland to both Mormon settlements in Utah, California (Trail), Oregon (Trail) as it includes South Pass through the Rockies that imminent wagon trains relied on and the key wayfaring resupply point at Fort Laramie in Wyoming. So potentially a Mormon nation like Texas, Deseret, where polygamy remains without the 1856 invasion by U.S. troops. California without a land route either becomes a British colony as their warships hoped when the Spanish there fell and the locals needed a new protector with seapower or it stays it's own republic and forges alliances with both the British and Americans, while Oregon and Washington states would remain part of British Canada. It includes the city sites of Casper, Cheyenne, Denver, Fort Collins, Santa Fe, Roswell...a lot of additional oil reserves in Wyoming, Colorado, Kansas, Oklahoma, and New Mexico unlikely to have been known at the time. I think the Colorado gold rush is in part or all of Texas's claim, a decade or so in the future.
Fort Laramie in Wyoming is an essential and key logistics base for the Army as well as the Oregon and California Trails, control of that (by negotiation as both Texas and the U.S. would have a heck of a time attacking, defending given the distance and paucity of other posts.)
So the U.S. would end in the shortgrass prairie states, British Canada'd be far stronger, the Texas Republic even more challenging to protect and develop, and two more independent but probably allied countries of California and Utah.
As President of Texas instead of Governor, Sam Houston likely could have kept Texas out of allying with either foreign power, the U.S. or Confederacy but might well have gotten involved driving the French out of Mexico instead (and grown Galveston tremendously as a direct seaport for British goods for the Confederacy instead of the smaller port at Matamoros on the Mexican side of the border.)
