This version of RetroArch does not have an Online Core Updater, which means, you can't download/update every Core. The Cores for this version are released as DLCs, this is most likely the reason why the Updater got disabled/removed.
Thankfully, you can easily "bypass" this problem. You only need to download the Cores from the official source, and copy it to a folder. However, and this is a big however, I'm not really tested every Core in the Steam version (maybe some of you did, then you can mention it on the comments down bellow), I only used PPSSPP and that's it. So if some of the Cores that you want to use don't work as intended, don't blame me!
Go to where your Steam installation folder is (mine is in the C: partition, C:\Program Files (x86)\Steam\steamapps\common\RetroArch) and find the folder called "RetroArch".
Choosing which Cores you want to use
Go back to the folder that you've previously extracted (RetroArch-Win64), and go to the cores folder. Choose which Cores you want to use and copy them.
Now that you choosed and copied the cores that you want to use, go back to where your RetroArch folder is, and copy the Cores to the "cores" folder!
Congrats, you're done!
You're done, now you have the Cores that the standalone version of RetroArch has!
Little side note
For some of the Cores you need additional files in the "system" folder. This is important, because some of them will not work without these files. I don't know the full list, but here are some, that definitely need those files (PCSX ReARMed, PCSX2, PPSSPP, Dolphin).
Here are some docs that you can use to correctly setup these emulators. It tells you what you need to copy and to where.