What does Mexico consider to be a valid travel document to enter and use in Mexico?

By air, per the TIMATIC database used by airlines, it's a passport or certain other booklet-type travel documents, except for Mexican citizens who can use, among others, a national ID card (only exists for minors aged 4-17), voter's card with photo or Matricula Consular (for expat Mexicans)

By land, the US passport card is also accepted, per the INM's FMM site

Your question clearly states

"...or Travel Document from their country to enter Mexico"

is required, as instructed by the Mexican consulate's (of San Francisco California's) directions. You have have not stated what your nationality or country's passport is, therefore it's really hard to predict what travel documents Mexico will honor for your country. Again, you don't specify, so I think your answer is currently impossible.

And yes, you are correct. Mexican travel documents include US Passport card, Enhanced Driver license and also the Nexus/SENTRI/FAST cards. If you intend to travel by air, a passport is always required. Any other type of transportation, you can use the non passport travel documents. If you're a US citizen, you must always present your passport no matter the method of travel.

This Frommer's article, "Can I Use a Driver License to Drive into Mexico or Canada?" also explains how to enter Mexico by land.

Now drivers need one of these to cross the U.S.-Mexico border by land:

• U.S. citizens can present a valid U.S. passport or passport card (click here to find out how to apply for those); an Enhanced Driver’s License (which is a new type of license that proves your citizenship—click here for information about those); a card from one of the Trusted Traveler Programs (NEXUS, SENTRI or FAST)
• You can also use one of these niche forms of identification, if you qualify: a U.S. Military identification card as long as you are traveling on official orders, a U.S. Merchant Mariner document if you are traveling in conjunction with official maritime business, a Form I-872 American Indian Card, or (if it's available) an Enhanced Tribal Card.
• U.S. and Canadian citizen children under the age of 16 (or under 19, if traveling with a school, religious group, or other youth group) need only present a birth certificate or other proof of citizenship. The birth certificate can be original, photocopy, or certified copy.
• U.S. Lawful Permanent Residents are required to present their permanent resident card (Form I-551) or other valid evidence of permanent residence status.
• Canadian citizens can present a valid passport, Enhanced Driver’s License, or Trusted Traveler Program card (NEXUS, SENTRI or FAST).
• Bermudian citizens are required to present a valid passport.
• Mexican citizens, including children, are required to present a passport with visa, or a Border Crossing Card.

The article also mentions that not all border crossings can read Enhanced Driver's Licenses.

If you have an Enhanced Driver's License, bear in mind that not all border crossings have the capability to read them.