respectively typically translates to
jeweils, neither seems optimal in your example. As @steros has pointed out in a comment, the translation ...
Tom und Jack spielen Fußball, respektive / beziehungsweise Baseball.
... suffers from a subject ambiguity that produces a reading in which both boys would play both sports. Pragmatics might filter this reading in the given example (for 'beziehungsweise' would suggest that both sports were related in some way, possibly to the extent that the latter were a specialization of the former, so since the relationship here is tenuous, the translation would probably work as intended). However, the preferred reading is much less pronounced if the sentence comes with very disparate leisure activities:
Tom und Jack spielen Fußball beziehungsweise Schach.
[Tom and Jack play football and chess, respectively.]
Note that the problem does not arise in a context that implies an ordering, as in
Tom und Jack wurden Dritter beziehungsweise Vierter.
[Tom and Jack ranked third and fourth, respectively.]
as different ranks cannot be held simultaneously.
A better translation would be:
Tom spielt Fußball, respektive Jack Baseball.
which resolves any ambiguity though it still feels a bit odd - you'd rather express the contrast with a conjunction:
Tom spielt Fußball, Jack hingegen Baseball. / Während Tom Fußball spielt, spielt Jack Baseball.
[Tom plays football while Jack plays baseball]
All grammaticality assessments based on native-speaker intuition, no formal references.