It could well be the first electronic "computer", but not what we today think of as a computer, in that it isn't programmable. It would be closer to a microprocessor, hardwired to do a specific job, and do it very well, but useless for anything else. That said, at the time, this would still have been a great advance. Technically, a large-scale block signal system is a computer, in that it uses the location and direction of trains to control the signals, and thus the movement of the trains it's tracking, but it doesn't have nearly as many inputs as a major terminal.
Railroads and "computers", of various forms, go back many years. One of, if not the, first large-scale commercial applications of technology for what we'd consider data processing was in railroad payrolls. No computers here, it was all punch cards, electro-mechanical card readers, and modified teletype machines, but it eliminated manually tracking hours and typing payroll lists. This was in the late 1800s, when pay was still in cash, often from pay cars.
If Mr. Babbage had built his steam-powered mechanical digital computer in the early 1800, I wonder what railroads would have used it for?