It's the Israeli PM because they have more 'power' than the President. Constitutionally it's the opposite with Palestine (practice may be different of course, especially in Gaza)", but it had to be one or the other. The current version dates from before recent events in Gaza. I'd point out that the game is hard enough to play as the Palestinians anyway without being lumbered with being a 'member' of Hamas - the game assumes that despite difficulties both sides are seeking peaceful co-existence, i.e a two-state solution.
'Intifadah' is just used as a symbol that peace efforts and relations have totally collapsed and been replaced with war and violence.
The game is about creating peace; the Palestinians can get a 'military' victory no more than the Israelis can.