You can use a CH341A programmer (or others which are more expensive) to program a large variety of such chips EPROM etc. You might need some adapter sockets and daughter boards for some chips. But you'd have to check what you'd need for that specific chip on that board. I used one once I burrowed from a friend to program a 5v chip so it went well.
Also some of the cheap programmers might put too much voltage on chip data lines and destroy some BIOS ICs. You put 5v to data lines of some 3.3v or 1.8v chips and they're toast. You can check chip voltage if you can find a datasheet online.
I'm not familiar with the BIOS IC on that board and the board itslef really or if there's any JTAG connector/jumpers. Some programers and some boards won't be easy to do in-circuit programming.
If you get a programmer without cables or a clip (or flimsy low quality nonworking clips) or if board has no JTAG or won't let in-circuit, the process might involve desoldering the chip from board, programming it and resoldering it back on. Are you confident you can do those things if it comes to that?
There's always risk of damaging the board beyond any possible repair while doing a desolder/resolder, IF it comes to that.
EDIT: Took a while to finish this post and saw Lutfij posted a video link. I'm certain it's from a good source and I'd suggest you watch such videos too. I'd also advise to be careful with possible dodgy donwload links.