Where does the phrase "MTG is not a game about reflexes" come from?
When people say "Magic is not a game about reflexes", they mean that you never have to react quickly to anything in the game. Beginners have frequent misunderstandings of the rules such has "Whoever announces that they're casting a spell first gets to have it resolve first.", which is incorrect because spells and abilities use the stack, and there is a turn-based priority system to ensure that only one player has the opportunity to take action at any one time. Similarly, people commonly believe some variation of "If you don't respond within five seconds, the spell resolves unopposed", which is simply incorrect: you have as much time as you need to respond to anything.

Brandon Burton has cerebral palsy. Brandon has competed at Worlds and the Pro Tour (two of the highest levels of competition in Magic). That goes to show that dexterity and reflexes are not a requirement to play competitively.