Is the subject of Emma only marriage and matchmaking?

Romance and marriage are definitely topics in Emma. In the nineteenth century when Emma was published, women had very few opportunities to earn money to support themselves; there were very few jobs available to women. Marrying well was one of the only methods women had to achieve comfortable homes. Some women (often from upper class families) wanted to marry individuals of equal financial and social status, so they could maintain their level of comfort and societal respect. Women from lower classes, too, tried to marry men of upper classes to increase their comfort and respectability. Sometimes women from wealthy homes fell in love with men with very little money or status. If a woman loved a man enough, she might be willing to sacrifice her material comforts for love. Families generally disapproved of their daughters (or their sons) marrying someone of a lower social or financial status.
In Jane Austen's novels, marriage is not simply a matter of love and romance; it is a financial transaction. This is clearly seen in the idea of marriage dowries, the gift of money that a bride brings to her husband, which is seen in Emma (and other nineteenth century stories). Emma, we find out, is an heiress of a substantial dowry. Men, such as Mr. Elton, try to woo Emma. It is likely that money is a part of his interest in her, since he immediately goes on to romance other rich women after Emma rejects him:

and if Miss Woodhouse of Hartfield, the heiress of thirty thousand pounds, were not quite so easily obtained as he [Mr. Elton] had fancied, he would soon try for Miss Somebody else with twenty, or with ten. (ch. 16)

Additionally, friendship is a significant theme in Emma. Early in the book, Emma is introduced to a new friend, Harriet Smith. She is highly involved in Harriet's romances, as she tries to help her friend marry a wealthy and respectable gentleman. Emma's ideas about love and marriage mature throughout the novel. She maintains a close friendship with her lifelong friend, Mr. Knightley. Emma has important conversations with Mr. Knightley throughout the book. Many of these talks help Emma to grow in her understanding of life and love.

A novel is a long and complex work, exploring the lives of imaginary people. Unlike an essay, a novel rarely has a single subject. Instead, literary critics describes novels as having a variety of themes.
Jane Austen's Emma, like most of her work, is set among the gentry of the English countryside. For the female characters of the book, one important goal is marrying well, but the novel addresses many different themes. The first is how pride and arrogance can blind people to reality. Emma's interference in others' lives (especially that of Harriet) is often willful or misguided and over the novel she learns humility. Other major themes include gender roles and the class and power structure of the gentry and the relationship between wealth and class. Finally, the novel is concerned with morality and the relationship between wisdom and goodness.