IF THEN ELSE Function in Mail Merge Doesn't Give The Option of <Field Name> CONTAINS

The reason you don't see a 'contains' option is because Word has no such field. That said, there are limited ways for testing whether a field contains something.

For example a field coded as:
{IF{MERGEFIELD MyField}= "MyText*" "True" "False"}
or:
{IF«MyField»= "MyText*" "True" "False"}
tests whether the results of the MERGEFIELD named MyField starts with 'MyText'
Similarly, a field coded as:
{IF{MERGEFIELD MyField}= "*MyText" "True" "False"}
or:
{IF«MyField»= "*MyText" "True" "False"}
tests whether the results of the MERGEFIELD named MyField ends with 'MyText'

You can also test whether the text you're interested in exists a pre-defined number of characters from the start or end. Thus, a field coded as:
{IF{MERGEFIELD MyField}= "???MyText*" "True" "False"}
or:
{IF«MyField»= "???MyText*" "True" "False"}
tests whether the results of the MERGEFIELD named MyField contains any three characters followed by 'MyText'
Similarly, a field coded as:
{IF{MERGEFIELD MyField}= "*MyText???" "True" "False"}
or:
{IF«MyField»= "*MyText???" "True" "False"}
tests whether the results of the MERGEFIELD named MyField ends with any three characters after 'MyText'

Note: The field brace pairs (i.e. '{ }') for the above example are created in the document itself, via Ctrl-F9 (Cmd-F9 on a Mac); you can't simply type them or copy & paste them from this message. Nor is it practicable to add them via any of the standard Word dialogues. Likewise, you can't type or copy & paste the chevrons (i.e. '« »') - they're part of the actual mergefields, which you can insert from the mailmerge toolbar. The spaces represented in the field construction are all required.