I was also trying to figure out why I didn't like this film as much as the 1987 incarnation of the story (which is some very pulpy schlock at times), and here are two specifics -
Lack of the Villain's Perspective - In the 1987 Running Man, we get a much more "behind the scenes" look at the show's production, and with it, the satisfying slow burn of watching the show-runner squirm as he slowly loses control of his creation (who was brilliantly played by Richard Dawson, an actual fucking game show host). That being missing from the story really hurts it.
Ultraprocessed Action Hero Syndrome - I've never seen much of Glen Powell in anything else, but there was something missing in his version of Ben Richards that kept me from buying into the character as anything more than a super generic action hero guy (not that this is his fault, could have been writing or direction).
The drums add crazzzzy tension to those battles and totally capture the "Well, I guess now we have to wait a whole 45 seconds before that giant salvo of missiles we can all see clear-as-crystal closes in another 2 clicks towards our position and absolutely nukes us" vibe of it all.
I've always thought that BSG's combat scoring was influenced by the combat music from the OG Homeworld game, which itself is ultra loosely based on the 70's BSG show.
I was also trying to figure out why I didn't like this film as much as the 1987 incarnation of the story (which is some very pulpy schlock at times), and here are two specifics -