A reinstall of the OS X does a similar function to a Windows repair install.
However -- you have manually removed at least one partition that is a normal part of a Windows install.
You had two very different systems, both bootable. Likely that removing the one system, and the other "adjustments" that you made, even with good intent, both damaged the install (like the boot blocks on Windows) for the Mac system as well. I would suggest that the best way to make sure everything is fixed, would be to start over completely, wiping the entire drive, and reinstalling both systems on a fresh drive.
A Windows repair install doesn't always fix things for the Windows install, and best practice (quickest way back) can be a wipe and restore.
BUT, you can also try a reinstall of the Mac software. Easy enough to do. Your Mac is a 2010, and not sure if it will do an internet recovery of the Mac system -- but you could try: Boot while holding Shift-Alt-Command-R. If you see a spinning globe, that would mean that internet recovery is working, and you can let that continue (it can take several minutes, can be more than 10 minutes), and you would get a menu that allows you to reintall OS X. This does not erase anything, just reloads the system on top of what you have. (If you don't see the spinning globe, then your Mac may not support Internet Recovery, and you will need to download the installer, and make a bootable USB drive from that. Reinstalling OS X might will fix the issue with the Windows install, but that would be a bonus (and some good luck, too!)
If Windows installer still complains - then likely your choice will be the full wipe and reinstall everything.
When you want to have two different systems that will both boot on the same hardware, everything about the install(s) needs to be right.
I can tell you that it's not always a simple operation to choose OS X/macOS to restart directly from Windows. It is easies to restart while holding the Option/Alt key, then make your choice from the Mac's boot-picker screen. When you have restarted into the Mac system, and you will be using the Mac before rebooting to Windows, select your boot drive in the Mac's System Preferences/Startup Disk pane. THAT is how you would avoid your Mac booting into Windows (or trying), because then you have selected the Mac boot drive as the default.