imm8 in ARM data-processing instruction
As in your quote, the immediate is rotated right by twice the value given in the rot field.
So for example in the case with rot=0001 the immediate value is rotated right two places causing two 1's to re-appear in the most significant position.
In the case of rot=1111 or 15 decimal, the rotation would be by 30 places.  Consider for a minute that rotating by 32 places would put the immediate value right back where it started, rotating right two places short of &quot;completing the circle&quot; back to the starting value yields an effective rotation left by 2 places, which is exactly what you see.
If that's still unclear, momentarily pencil in a hypothetical case as if the illegal value rot=10000 (16 decimal) were actually legal. You'd then see that this yields the same result as the legal value rot=0000, making it unnecessary.  You could also fill in all the intermediate possibilities as desired.