I say sort of, because the pawns actually move a little different than their chess counterparts and Bosworth also doesn't have any of the special moves -- en passant and castling -- of chess.
I think Bosworth could have just as easily been called "knife fight chess" because that's how it really strikes me. The main battlefield is just a four-by-four square -- a quarter of a chess board -- with an additional four-square "field camp" for each player for most of the game. Into this tiny battle field will foray up to 32 (in a 2-player games), 48 (3-player) or 64 (4-player) chess pieces!
It's a cvery close-range and chaotic fight that will leave players weighing captures and their relative values nearly every turn. But evaluating those captures by the tried-and-true valuations of regular chess is a mistake. The real values of the pieces in Bosworth are different.
In standard chess a pawn is usually valued as a "1." Knights and bishops are "3," with some authors giving the Bishop a slight edge. Rooks are usually valued at "5" while the queen is considered to be worth 9 pawns. The king, naturally, has an infinite value in regular chess because checkmate ends the game.
The Bosworth knight retains its value of a "3," largely because of its ability to jump, which has a heightened value on such a congested board. The knight's mobility is constricted compared to regular chess because it's almost always close to an edge. Only from the center four squares can the knight enjoy the full 8 potential landing squares that it enjoys from 16 squares in regular chess. Still, the jump makes up for that and a Bosworth knight is still worth three pawns so long as the board is crowded. In a 2-player game, however, I'd rate a knight as worth just 2 pawns. The jump move is more constricted by the board edges, the board is less crowded and the knight's moves more predictable.
The overall effect is that pawns in Bosworth play a much more aggressive role than they do in standard chess. They essentially start at "mid-board" in standard chess terms. Pieces, other than the queen, are relatively less valuable than they are in standard chess, especially in the 3-player and 4-player set-ups. More important than the mere value of the chessmen is the timing and placement of them.