It should be "I suggest the players study..." 'The players' is the plural subject noun of the verb 'to study', which should be in the third person plural singular.
'Players' normally 'play a game', not 'a play' - actors 'act a play', and a play does not usually have 'rules'. However, in US English, players might 'make a play', which is a discreet piece of action within the game (for example, in American Football).
'Them' is perfectly correct - it is a pronoun referring back to 'the players'.
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