Jacy,
There is no specific "law" that says, "Thou shalt attend all church functions!" However, one would rightly assume that if one is regenerate, has come to Christ in repentance and with true saving faith, that person would be drawn to the Church, which is the body and bride of Christ.
Secondly, from this I would expect that any professing believer would yearn to worship God in the company and fellowship of other believers, aka: corporate worship. This would mean meeting together at the appointed times on the Lord's Day; both morning and evening services if they are available.
Thirdly, extra activities hosted by the Church, e.g., Bible Studies, Sunday School, prayer meetings and such; NOT barbecues, pot luck suppers, raffles, etc., some of which are to be shunned, would be determined by work and family schedules.
Fourthly, from what you wrote it would seem reasonable to presume that the church in question does not observe the Sabbath, i.e., the Lord's Day. Even if the church doesn't officially observe the Sabbath as part of the moral law of God (Fourth Commandment), it should at least set the day apart as that which was created for man to have the freedom to worship God, and delight in the things of God. (cf. Isa 58:13, 14)
NOTE: Historically, some Baptists have not observed Sunday as the Sabbath (Fourth Commandment), but they have set the day apart as a day for worship, study and works of mercy and necessity. That is, their observance of the day was identical in practice to those who considered Sunday the NT Sabbath... cf. John Bunyan. The "official" statement of the Sabbath of the Reformed Baptists is found in
The London Confession of Baptist Faith, Chapter XXII "Of Religious Worship and the Sabbath Day", articles VII and VIII.
Fifthly, it would seem this Elder has little regard for either observing the Sabbath Day as part of the moral law of God nor as a day created for man for the purpose of worshiping God and spending the day in delighting in Him, etc. If this man were an Elder in my church he would be set down and informed of his sinful behavior. Should he continue to neglect the Day by being involved in worldly recreation, etc., he would be put under discipline and possibly be removed from office if repentance was not forthcoming.
Lastly, since I hold to the "traditional" view as found in all the Confessions of the churches which came out of the Protestant Reformation to one degree or another, man has GREAT liberty in regard to the Sabbath Day. He is free to cease from all his regular labors and recreations and join with the people of God to offer up worship to Him in word, praise, prayer and song. We are free to do all manner of works of mercy to those in need; visit the sick, infirm, needy, poor, those incarcerated in prison/jail, feed the hungry, aid the elderly, etc. We are also free by God's mercy to do works of necessity, e.g., doctors, nurses, pharmacists (regulated if possible), etc. Some of us here have rejected work that has required we work on Sunday. And some have been fired for not working on Sunday. In short, we are free to worship God for the entire Day and express our love to our neighbors on that day. We are free to focus our entire beings; mind, soul and heart on our great God and our Redeemer Jesus Christ. We are free to spend time with our families to instruct them in the things of God. You see, there is incredible liberty in Christ in regard to what we are free to think and do on His Day... because the Sabbath was created for man.

In His grace,