Actually, West Ham fans bang on about the ‘West Ham Way’ more than any other teams fans do about their supposed characteristic style (for example, only properly ancient Evertonians still crap on about the ‘School of Science’).
The West Ham Way is of course elusive and undefinable, except that it seems to insist on tricky wingers who run at teams and/or cross a lot, and an absolute nutcase somewhere in defence. Apart from that, it seems to advocate passing that is simultaneously passing and direct, defensive midfielders who like to attack, mobile and dynamic, yet also patient, with a languid, indolent looking playmaker who can only conjure some magic when he really needs to, a team that is structured yet highly fluid.
No real surprise that they have given up crapping on about whether Moyes is true to the West Ham Way ™ now that the results are really good.