Planeswalkers

does the old "remove from the game" mechanic get replaced by "exile" or is it a different mechanic entirely?

wondering if Ashiok Nightmare Muse planeswalker would be able to interact with cards that have been "removed"

Well, since "remove from game" was itself removed from the game, you should never encounter that scenario. I can't confidently say that 100% of the carsd that previously read "remove from the game" now say "exile", but certainly they all no longer contain "remove from game".

You can use Wizards' Gatherer database to see the Oracle Text on any card, which will show if it has had any changes and what they are. Here is a good example: Swords To Plowshares
That's an older version of Swords to Plowshares. If you toggle the Orace Text switch it will flip between showing the original and the updated version of the card, which in this case does indeed replace the old "remove form game" with "exile".

cool cool thanks for explaining this

If a card has text that seems obsolete or weird always check gatherer.wizards.com for the oracle text.