What does backslash dot mean as a command?

A backslash outside of quotes means “interpret the next character literally during parsing”. Since . is an ordinary character for the parser, \. is parsed in the same way as ., and invokes the builtin . (of which source is a synonym in bash).

There is one case where it could make a difference in this context. If a user has defined an alias called . earlier in .profile, and .profile is being read in a shell that expands aliases (which bash only does by default when it's invoked interactively), then . would trigger the alias, but \. would still trigger the builtin, because the shell doesn't try alias expansion on words that were quoted in any way.

I suspect that . was changed to \. because a user complained after they'd made an alias for ..

Note that \. would invoke a function called .. Presumably users who write functions are more knowledgeable than users who write aliases and would know that redefining a standard command in .profile is a bad idea if you're going to include code from third parties. But if you wanted to bypass both aliases and functions, you could write command .. The author of this snippet didn't do this either because they cared about antique shells that didn't have the command builtin, or more likely because they weren't aware of it.

By the way, defining any alias in .profile is a bad idea because .profile is a session initialization script, not a shell initialization script. Aliases for bash belong in .bashrc.

The \. is a "literal dot", i.e. just a dot. It will be taken as the standard . command (similar to source in bash).

The POSIX standard has this to say about this (my emphasis)

A <backslash> that is not quoted shall preserve the literal value of the following character, with the exception of a <newline>. If a <newline> follows the <backslash>, the shell shall interpret this as line continuation. The <backslash> and <newline> shall be removed before splitting the input into tokens. Since the escaped <newline> is removed entirely from the input and is not replaced by any white space, it cannot serve as a token separator.

The dot character can be aliased:

$ alias .='echo hello'
$ .
hello

which means that \. would avoid using the aliased version of the . command, because,

After a token has been delimited, but before applying the grammatical rules in Shell Grammar, a resulting word that is identified to be the command name word of a simple command shall be examined to determine whether it is an unquoted, valid alias name.