I know this is an old thread... but it left a few open questions... these are now answered. No for Tesla. Direct copy from the PDFs on the LDPLI (State of TX) web site:
1.6 REQUIREMENTS Additional criteria that apply are discussed below.
a. The vehicle must be purchased or leased from a licensed new vehicle dealer or leasing company in Texas. Vehicles purchased directly from the manufacturer or an out-of-state dealer not licensed to sell or lease new vehicles in Texas are not eligible for a rebate.
Thanks for the update. So not only does this benefit the dealerships and their monopoly, but they are also helping the oil companies by not providing rebates to customers who want to buy an EV. NOT. COOL. Another reason this state is ass-backwards.