The formation of the carbonyl group is a gain in thermodynamic stability over the vinyl ether. In your example, the monosubstituted alkene is a "wash". In any case, the alkyl substitution pattern of the non-enol ether double bond is not a problem.
The heat of this Claisen rearrangement, first conducted by Hurd and Pollack1 in 1938, can be calculated by determining the heat of formation (ΔHfo) of allyl vinyl ether (1) and 5-hexenal (2). Heats of formation of allyl vinyl ether (1), hexanal (3), 1-hexene (4) and hexane (5) are known (NIST and Chemeo). These heats of formation are shown in black. However, the ΔHfo of 5-hexenal (2) is not accessible in tables but it can be calculated. The heat of hydrogenation of monoalkyl substituted alkenes is ~125 kJ/mol (~30 kcal/mol). The reduction of 1-hexene (4) to hexane (5) is -124.6 kJ/mol, which is computed from the respective heats of formation of 4 and 5. Applying this heat of hydrogenation to the reaction 2 ---> 3 gives a ΔHfo of -128.2 kJ/mol for 5-hexenal (2). Accordingly, the Claisen rearrangement of allyl vinyl ether (1) is exothermic by -100.6 kJ/mol.
1. C. D. Hurd and M. A. Pollack, J. Am. Chem. Soc., 1938, 60, 1905.