It seems that the discussed scenario uses a custom Kendo UI theme. In such cases it is better to send a runnable example (or a live URL), that includes all the custom CSS code, which we don't have. I tried to reproduce the described issue by using some custom styles, but to no avail.
Generally, all browsers have issues with zoomed content and sub-pixel rendering, which can be exhibited in random overlapping or disappearing content at certain zoom levels, but not at others. Sometimes a possible workaround is to replace styles that use relative units (em's) with styles that use absolute units (pixels). For example, try setting all Menu-related paddings, font-sizes and line-heights in pixels.
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