I believe that establishes your point to a reasonable degree, though it does not establish it as the sole reason. What Boothe said after he had shot Lincoln cannot be dismissed. Perhaps Boothe regarded this move by Lincoln as "Tyrannical".
Given the mentality of the time, It is likely that he did.
His initial plan, as testified to by his co-conspirators at their trial, was to kidnap Lincoln and hold him for ransom. There was at least one attempt to do that which was foiled when Lincoln suddenly changed his daily schedule.
The night of that speech, Booth's plan changed to assassination, not just of President, but of the Vice President and the Secretary of State.
If Lincoln was the 'tyrant' the both Booth and you seem to think he was, Booth who was well known to be in favor of the Confederate cause, would not have even been on the streets. He would have been locked away or a dead man by then. Booth never made any secret where his sympathies laid.