No. A game like BioShock requires a lot of system resources to maintain decent frame rates and a VM is not going to cut it.
BioShock was created for Intel CPUs so even if CodeWeavers' CrossOver Mac would allow the app to run, performance may still be a huge issue. This is the best option that has any hope of working unless 2K Games decides to make an M-series port (doubtful). CodeWeavers does provide a free trial period.
Unless the game is available from the Apple App Store specifically for an M-series Mac, then be very careful about purchasing any game from any other source. Games are not like standard apps when it comes to compatibility. Games usually require a lot of system resources so any compatibility layers will tend to have a negative impact on game performance. Plus games are coded to use very specific CPUs & GPUs.....so using anything else will likely result in issues of some sort. As you have discovered with BioShock Infinite, you cannot go by the system requirements which mention macOS version XX+ or CPU/GPU YY+.
Keep in mind Macs are and have never been a gaming platform/computer. Yes, some games are available for certain Macs and will run fine, but you must do thorough research to determine if a particular game will work with a specific model Mac and its version of macOS and how well it performs. Be careful since some people may say a game works fine for them even if it is stuttering at low frame rates....some people don't care.
If you want to play games on a computer, then a Windows gaming system is the best option. A dedicated game console such as XBox or PlayStation are usually the best option so you don't have to deal with Windows issues & hardware issues/compatibility.
Edit: Actually just stumbled across this site which has one review where a user mentions BioShock Infinite runs fine using an M1 Mac and Parallels 16 (take it with caution since only one person has provided the rating):
https://www.applegamingwiki.com/wiki/BioShock_Infinite