Mechanism of synthesis of allene
This is the Skattebøl rearrangement, the first step is of which is a lithium-halogen exchange to form a carbenoid. A mechanistic study of the rearrangement of monosubstituded lithium bromocyclopropylidenoids found that allene formation can occur either in a concerted (Scheme 2) or step-wise (Scheme 3) fashion depending on the ability of the substituent to stabilize the intermediate carbene$^{[1]}$.


  


The study found that electron donating groups (like the methyl groups in your example) lower the barrier to allene formation. For several EDG-substituted species, the free carbene structure 14 could not be found as an energy minimum and all attempts to locate these structures lead directly to allenes. This means the stepwise mechanism does not play a role in the Skattebøl rearrangement for EDG-sbustituded species$^{[1]}$.



$[1]$ Azizoglu, A.; Balci, M.; Mieusset, J.-L.; Brinker, U. H. The Journal of Organic Chemistry 2008, 73 (21), 8182–8188.