To get a bit technical, the so-called ANSI encoding isn't really an ANSI encoding. It's the Windows-1250 encoding for Central European languages, which is loosely based on a proposed ANSI standard and the ISO-8859-2 encoding for Central European languages. Microsoft once mislabled them, acknowledged their fault, but the misnomer stuck. For example, the character is encoded in your file at 0x9a, in the standard at 0xb9 and in Unicode at 0x0161. Right now, the Linux applications recognise the subtitle files use a legacy 8-bit encoding, but they assume it's the ISO-8859-1 encoding for Western/Northern European languages, not the Windows-1250 encoding. Notepad++ in wine thinks it's the Windows-1252 encoding, almost identical to ISO-8859-1.
I don't know Rhythmbox or VLC very well, but there must be a menu somewhere to tell the program what the encoding of the subtitle file is. Else, you can convert the file to UTF-8 encoding (which is pretty much the standard, not only in Linux but on the web too). The command
should do the trick. A text editor can do it too. In gedit you can specify the encoding when opening a file using the menu (not when double-clicking the file in the file manager). Then, without editing, save the file, selecting UTF-8 encoding.
iconv -f WINDOWS-1250 -t UTF-8 -o <output file name> <input file name>
I don't know about the crashes of your Rhythmbox. Someone else may help you with that.
One kind request: when posting large screenshots it's better to include them as attachments instead of in-line. Not everyone has a fast internet connection.