No, that is not an inductor, that is MOSFET or big bro of the transistor. This is a pretty common one, again easily replaceable. These usually don't go bad so early, especially these arrow branded ones last at least 10 years even during high usage.
Get it changed, don't pay a high amount as the MOSFET costs 50rs( 20/piece If bought in bulk) so labour costs must not be that high, considering he needs to do chip level repair. Ask the guy to also do a regular board checkup, as may be due to some other fault such as fluctuation from PSU this got damaged.
PS:- inductor coils are actually those big boxes at side with labelling like R50.
View attachment 21175
These are also inductors used and in the previous pic, it looked similar to this.