Yes But...
The provider can include anything in the ToS document that s/he chooses to. It may or may not constitute a binding contract, and even if it does, all of its provisions may or may not be enforceable, depending on the laws of the jurisdiction involved.
The ToS linked in the question includes the provision:
BY ACCESSING OR USING THE SITE OR SERVICES, YOU AGREE TO BE BOUND BY THESE TERMS AND SUCH OTHER TERMS, CONDITIONS, POLICIES, AND DOCUMENTS THAT MAY BE INCORPORATED HEREIN BY REFERENCE,...
That kind of "accept by access" provision does not create a binding contract at all in many jurisdictions. There must be a positive affirmative act, such as signing a name, checking a box, or clinking an "I accept" button in such jurisdictions for the ToS to be a binding agreement.
In a fair number of jurisdictions, there must be consideration for a ToS to act as a valid contract.
Even where there is a binding agreement, a party must usually show damage to sue successfully. The website operator can reasonably argue that its interests are harmed by the use of automated means to access the site, or by bulk downloads. It is hard to see how the operator could argue reasonably that the use of a non-Microsoft mouse harms its interests.
So, the site can request or purort to require whatever the operator chooses. Whether a suit to enforce such a requirement would be successful is a very different question. A suit to block automated access has, IMO, a fair chance of success, and some precedent in its favor. A suit to block access by a user using a Logitech mouse IMO does not.
Also, some particular provisions may be barred by law, although none of the ones mentioned in the question fall into that category as far as I know.