Does the Windows license allow the use of pre-installed fonts in images on the site?

Theme Lebedev spoke about the claims made by his studio precisely because of the fonts that were used in a number of works. So you should carefully read the license agreements.
As for Windows, at one time I had to face the fact that MS promotes a policy like "fonts are licensed from their creators or copyright holders" and can be freely used only inside the system and its applications.
In practice, this means that you can safely use fonts, say, to print a presentation and go to a conference with it, but you are guaranteed not to use it for commercial purposes (we had to change the font in the trademark to OFL three years ago). Again, the probability of a claim against a private user is much lower than against a company.
Based on this, technically, you are violating the licensing rules. by doing as you described. But if the site is non-commercial, its traffic is not excessively high, then the probability of a claim is low.
And better - use OFL fonts

Specifically for Arial, as far as I understand, is possible, including for commercial purposes, but you can not print the font in the form of images and use them as a replacement for the font.

The copyright holder and the license can be found in the font file itself in windows/fonts, in particular for Arial it is indicated there:

Copyright notice: The Monotype Corporation. License description: "...You may only (i) embed this font in content as permitted by the embedding restrictions included in this font;".

It is not clear what the restrictions included in this font are. This is probably a reference to the full font license, which can be found on the official Monotype website:

Http://www.monotype.com/legal/eula/

FONT SOFTWARE END USER LICENSE AGREEMENT

You may embed static graphic images into an electronic document, including a Commercial Product, (for example, a "gif") with a representation of a typeface and typographic design or ornament created with the Font Software as long as such images are not used as a replacement for Font Software...