The longest possible chess game

Playing with a real board was a useful way for me to wrap my head around this problem and solution. You just tell yourself that each pawn move and capture represents the 49.5 moves that came behind it.

Any move that isn't a capture or pawn move you can ignore.

When you do that, here's a representation of what the longest game looks like:

(Hard to notice, but moves 29, 109, and 171 marked with "switch")

No.

I mean, do you even read?

Tell me, what's the point of me trying to have a conversation with someone who doesn't understand English?

Exactly, you have no answer.

Oh, you must not have known me very long. Sometimes I'm not very nice.

I have no idea. How many moves are possible? GM Yasser Seirawan gives the number of possible moves in a chess game at time 26:26 in this video - 10 to the 56th power!! (By the way, a very funny video as he talks about how poorly he played some of his earliest games, including a checkmate on him that wasn't, that he agreed with!)

Claims under the 50 move rule are optional (and no longer included in the FIDE basic chess rules).  The 75 move rule included in the competition rules is mandatory, so in either case your expectation is correct. 

Under basic rules infinite games are allowed (but none of these have finished yet). This was also true under previous basic rules because claims under the triple repetition rule included in those were also optional. 

For chess.com it's 5898.5 moves because (unlike before) they auto claim it on move 50.

For the 75 move rule it's 8848.5 moves 

But that means that the games on chess.com are strictly speaking not chess games since they don't follow the laws of chess.

Legalistic ideologies are intrinsically dumb.