Using the hack suggested by @andre314, you can use
DynamicModule[{x = {0.1, 0.}, a = 1},
Pane[Pane[Dynamic[Plot[Sin[x (1 + a x)], {x, 0, 7}], {x, 0, 6}],
ImageSize -> {Full, 1100}, AppearanceElements -> None,
Scrollbars -> None], ImageSize -> {Full, 1000},
AppearanceElements -> None Scrollbars -> {False, True},
ScrollPosition -> Dynamic[x, Function[If[#[[2]] >= x[[2]], a--, a++];
x[[2]] = Mod[x[[2]] + 0.001, 0.1, 0.1];]]]]
which can produce different curves on mouse scrolling

(a few mouse scrolls...)

and for the chess example, save e.g. this chess gif as chessgame.gif, then try
frames = Import["chessgame.gif"];
(*This gives periodic boundary conditions to the scrolling*)
cycle[a_, frames_] :=
Module[{},
If[Mod[a, Length@frames] > 0,
out = frames[[Mod[a, Length@frames]]]];
If[Mod[a, Length@frames] == 0,
out = frames[[Mod[a, Length@frames] + 1]]]; out];
(*This gives the animation itself*)
DynamicModule[{x = {0.1, 0.}, a = 1},
Pane[Pane[Dynamic[cycle[a, frames]], ImageSize -> {Full, 1100},
AppearanceElements -> None, Scrollbars -> None],
ImageSize -> {Full, 1000},
AppearanceElements -> None Scrollbars -> {False, True},
ScrollPosition -> Dynamic[x, Function[If[#[[2]] >= x[[2]], a--, a++];
x[[2]] = Mod[x[[2]] + 0.001, 0.1, 0.1];]]]]
which gives a scrolling chess animation

(a few mouse scrolls...)
