The normal loss condition of having zero or less life happens only once per check of state-based actions. The Transcendence loss ability triggers continuously in an infinite loop, with no way to continue playing.
The loss to zero or less life happens due to state-based actions. They are checked often, but not infinitely often. They are checked whenever a player would gain priority, which happens only at specific points during any given turn.
117.3a The active player receives priority at the beginning of most steps and phases, after any turn-based actions (such as drawing a card during the draw step; see rule 703) have been dealt with and abilities that trigger at the beginning of that phase or step have been put on the stack. No player receives priority during the untap step. Players usually don’t get priority during the cleanup step (see rule 514.3).
117.3b The active player receives priority after a spell or ability (other than a mana ability) resolves.
117.3c If a player has priority when they cast a spell, activate an ability, or take a special action, that player receives priority afterward.
117.3d If a player has priority and chooses not to take any actions, that player passes. If any mana is in that player’s mana pool, they announce what mana is there. Then the next player in turn order receives priority.
117.5. Each time a player would get priority, the game first performs all applicable state-based actions as a single event [..]
Platinum Angel prevents that single loss event each time a player would gain priority, and that's that.
The loss ability of Transcendence, however, has a state trigger. It will trigger whenever the game state in question has been reached and no instance of that ability is currently on the stack. As soon as the trigger leaves the stack (or doesn't enter it) for any reason, and the game is still in the necessary state, the ability will trigger again right away, without anyone being able to react. Platinum Angel's ability removes the Transcendence trigger from the stack by preventing it. The Transcendence ability never enters the stack, it immediately triggers again, and no player will gain priority, resulting in a draw.
603.8. Some triggered abilities trigger when a game state (such as a player controlling no permanents of a particular card type) is true, rather than triggering when an event occurs. These abilities trigger as soon as the game state matches the condition. They’ll go onto the stack at the next available opportunity. These are called state triggers. (Note that state triggers aren’t the same as state-based actions.) A state-triggered ability doesn’t trigger again until the ability has resolved, has been countered, or has otherwise left the stack. Then, if the object with the ability is still in the same zone and the game state still matches its trigger condition, the ability will trigger again.
614.6. If an event is replaced, it never happens. [..]
603.3. Once an ability has triggered, its controller puts it on the stack as an object that’s not a card the next time a player would receive priority.
So what happens is, Transcendence triggers. The next time a player would gain priority, the Transcendence trigger wants to enter the stack, but Platinum Angel prevents that. Transcendence immediately triggers again, Platinum Angel prevents it again, and so on, before the player can ever gain priority. Therefore, it's a draw because there is a loop with only mandatory actions.
721.4. If a loop contains only mandatory actions, the game is a draw.