The site should use FIDE rules. It's absurd that with this site's rules, black can turn a loss into a draw by deliberately letting his time run out in the top position , but loses in the bottom position if his time runs out:
There are three rule sets to consider: FIDE, USCF, chess.com
In the first position, if it is Black to move and Black flags then only FIDE gives the win to White
In the first position, if it is White to move and White plays Bc3+ then White has a forced mate and both FIDE and USCF will give a win to White if Black opts to flag while chess.com would ignore the Black pieces other than the king and rule it a draw (K+B vs K).
In the second position White is in check and the only legal move is Kh1. If Black flags than FIDE and USCF would rule it a loss (because Qfc2 allows the White pawn to be advanced and eventually queen, or a draw if the d5 king and c6 queen were swapped since there would then be no legal moves that neither capture the pawn nor stalemate/checkmate the White King) while chess.com would simply ignore the black queens regardless of their position and rule that K+P can win against a lone king.
chess.com turns some FIDE draws into decisive results and some FIDE decisive results into draws.
I wonder how easy it would be to write a program to recognize that White Pa2, Pa5, Pc2, Pc5, Pe2, Pe5, Pg2, Pg5, Bc1, Kh1 vs Black Pa6, Pc6, Pe6, Pg6, Ke8 is an unchangeable draw even though White is a Bishop and four Pawns ahead.
The site should use FIDE rules. It's absurd that with this site's rules, black can turn a loss into a draw by deliberately letting his time run out in the top position , but loses in the bottom position if his time runs out: