Yes the video game plays like the boardgame, but a caution, the level of play vastly differs. those of us that have been playing the board game along time...and I mean a long time, 20+ years for me now, see the videogame as not even a little bit competitive (vs computer). the AI does not understand how to the play the game competitively.
This is going to sound like a brag, but take it as a critique of the AI, but on the hardest level of difficulty I can count the number of games lost on one hand (of probably 500+), and usually to wood elfs. the computer does things in the wrong order or wrong priority compared to someone who would play competitvely. so please be aware of that. order of operations is what BB is about. when to move what and at what level of failure. the computer game does not get that.