"Military Class" lol
Saying "tested to MIL-STD-810G" means very little. MIL-STD-810G is a giant document that establishes test PROCEDURE, and suggested test limits for many cases. You could use ESTI 300-019-2-3/-7, IEC 60068-XX or ISO procedures and still hit the same level of quality / robustness and in fact, the limits for many tests are nearly identical across these documents (free-fall drops, temp & humidity, thermal shock, etc). MIL-STD-810G is freely available online, and the document title is "DEPARTMENT OF DEFENSE TEST METHOD STANDARD - ENVIRONMENTAL ENGINEERING CONSIDERATIONS AND LABORATORY TESTS".
A big appeal of MIL-STD-810G is that it is FREE, whereas you have to pay for the ETSI, IEC and ISO specs. I've dealt with a lot of this on a daily basis at work for the better part of a decade, so take it from me that saying "MIL-STD-810G compliant" is mainly a marketing tactic, and if anything it means that MSI saved ~$1000 by not having to buy ETSI / IEC documents lol.